Having written the above reply, I am left wondering if we go back to the outbreak of open civil war in England whether the anti-monarchial faction might indeed have somehow wound up being dominated by, or anyway containing as indispensable factions, a radical "cantonial" faction united by shared program and providing an alternative "model army" grounded in radically democratic local regimes, where village self-government provides reasonably well trained, disciplined after a fashion, politically reliable fighters that such commanders as Cromwell perforce must rely on for victory and face as irremovable players after putting down the royalists. If a fair number of the English population at that point runs their government and law locally, while continuing to recognize the need to remain in federal union with the rest of England, then we would have a collective constituency for radical democracy and an argument that neither lords (formal or informal) or kings are needed.
I am not studying up on the details of how Switzerland evolved its own federal canton system in part because I don't believe for a moment that anyone (or anyway, very few people) in England would be consciously looking to the Swiss example. They could and did study up on many possible systems but I don't think it would occur to them to look to a bunch of rustic mountain men way off in distant central Europe and largely "Papist" at that. I don't recall any American or other revolutionary radicals of later centuries systematically modeling anything after the Swiss example, when it had been tested by further centuries of survival--indeed, Napoleon Bonaparte made short work of sweeping it all away at least on paper and imposing a "Helvetican" unitary "Republic;" the Swiss had to reconstruct something resembling their own system again after the French imperial system fell apart I gather, and indeed faced some severe crises in the middle of the 19th century.
But I do wonder if a parallel evolution might be possible, and if so whether England would thereby be diverted from the major role it played in the Modern period or perhaps might hit on either squaring the circle of an authoritarian and rather ruthless collective global empire on a nominally democratic basis, or even hit upon playing a similarly major geopolitical, economic and demographic powerhouse role with much more democratic mechanisms throughout the system--which would I think put global capitalism on a rather different basis in key phases of its general global evolution.
A cantonial Commonwealth would be quite different already in the mid-17th century; where the Commonwealth functioned largely as a unified kingdom in terms of European international power politics in the early "Westphalian system" age of emerging nations, perhaps we'd see wild contradictions in overall English policy as various port towns adopted different, conflicting policies. Would there be any unified English/"British" navy at all, for instance?
"British" in scare quotes refers to the fact that OTL there was no formal Act of Union joining Scotland to England until the early 18th century; I don't know how relations between Scotland and England worked when the parties dominating Scotland concurred with the victorious Roundheads of England that Charles was no monarch of theirs, but no formal act of union then tied Scotland, which I infer had no monarch of its own and accepted Charles II along with England, to the more populous southern nation in the island. If England goes "cantonial," with hundreds of little polities of various sizes united loosely in a great English confederation, do the Scots similarly adopt such cantons and participate in a general "British Commonwealth," and if major polities of Scotland do so, does all Scottish territory play along or will there be zones which either operate as a rival republic or adopt a king of their own, perhaps none other than Charles II himself? And anyway what the heck did happen OTL, where Scotland as a whole certainly never adopted any interim monarch nor did any pretender effectively control any major part of Scottish territory as far as I know, yet as far as I know the Scots were not participating in the Parliament in London either--did Cromwell claim to be and was recognized as Lord Protector of Scotland too, or what?
Anyway leaving this lacuna in my education aside, thinking of England as a patchwork of largely autonomous local cantons, I suppose some of these would be radically democratic, with effectively universal town meeting governance by the whole adult male population more or less deferring to this or that factional leaders who, knowing the relative and perhaps shifting balance of power among them, more or less amicably negotiate consensus rules and choose delegates, with or without formal acclimation by the gathered folks, to go to Parliament, while other places might be more formally aristocratic, with certain burghers or squires understood to be responsible for and in charge of the general populace and either meeting as a senate of sorts or simply deferring to a consensus local Protector who handpicks his agent in Parliament or drops in as the formal Member himself. For radical democracy to persist in any cantons I suppose there has to be a general assent in the Commonwealth as a whole that such extremism is acceptable at least as long as it doesn't get too unruly, and the magnates of the more authoritarian bailiwicks have to tolerate a certain degree of pro-democratic agitation and accept the pretensions of the "mob" to have some right to demand some accounting of what the Great and Good they defer to are up to and doing for them lately. Otherwise I expect that one by one, the radical zones would have more orderly and safe overlords imposed on them piecemeal and the democratic principle would be snuffed out--whereas I don't think it is inevitable, even if the Commonwealth affirms all authority devolves from the total populace, that all zones will go fully democratic, though the "threat" of the mob asserting itself might indeed make a squirearchy or senate of rich burghers keep their political ears to the ground and in fact act to keep a consensus majority of their subjects reasonably satisfied with things as they are.
On such a basis as this, perhaps the Commonwealth Parliament can defer much of what they had to legislate on and provide concrete executive machinery for down to the cantonial local self-administration, and much coordination of diverse and contradictory local rules can be done collectively, in committee or by floor debate, by Parliament as a whole, if the various cantons do accept Parliament's upshot rulings as final.
There still would be a need for some central executive power I suppose--OTL the modern Swiss system provides a collective though small Executive Council, with its members carefully and deliberately balanced in partisan composition. It would be possible to also provide a supreme chief executive who must answer to such a council as well as to Parliament as a whole, but this might be avoided to prevent the nucleus of a new monarchy from forming.
Now OTL, the evolution of the British parliamentary constitutional monarchy system was deeply intertwined with that of global capitalism. Basically, the leaders of the Commons believed themselves to be primarily answerable to the most powerful and wealthy sectors of the British system, with obligations to the commoner majority being as much about keeping them subservient as about looking to their interests. It was only gradually that various sectors of the working classes were systematically included in the electorate, on a selective basis of qualifications, and the entire process was somewhat ramshackle, with different constituencies having different degrees of more or less popular franchise, not to mention these constutuencies varying wildly in actual total population, from "rotten boroughs" with some nominal lord having the sole discretionary vote and no actual inhabitants whatsoever, to great cities that had grown up where hundreds of thousands were represented by another MP having the same weight as the handpicked Member chosen by some lord of a vanished ghost town.
If a cantonial basis for a Commonwealth Parliament exists, I would expect a certain rough and haphazard coordination of population with membership to evolve over the centuries (assuming the system survives as well as say the Swiss one did OTL); if some town that once clearly had a plain right to send two or three members shrinks down, sooner or later it will shed these members and in time its territory be swallowed up in some neighboring zone the remaining inhabitants have shifted their ties to, while a growing town will have influence in the private sphere that gives it leverage to pick up new members, perhaps with some quid pro quo constraining their selection to be either more democratic or less so, depending on which way the political winds are blowing that decade. This process might relieve any pressure for systemization of constituency size, with the rough sorting deemed sufficient to achieve fair representation overall.
OTL, with Parliament and the local rule both coordinated to be preoccupied with the interests of the well off, capitalism evolved with persons of wealth being able to largely prevail. Would cantonial organization, reserving key powers of governance to local regimes, serve to totally block such evolution, or would the democratic principle be inevitably repressed in favor of a de facto rule by gentry? I suspect a compromise might emerge, which would somewhat slow the evolution of capitalism as we know it and perhaps systematically divert it toward a more social democratic path. Some rural cantons might become conservative peasant republics, sticking to traditional norms and thus developing productivity more slowly, and if it is true that only privatization on OTL lines can open the way for progress in agricultural productivity, such zones would come under fatal pressures. But if in fact there are other paths to collective gains in productivity with more intensive farming guided by democratic consensus, we might see ATL forms along what we might retrospectively label as "syndicalist" collectives meeting and exceeding the needs of rising local populations and marketing surplus goods for sale to urban populations as internal improvements aid better communications via canals and later railroads. Meanwhile others might follow capitalist logic but their "surplus population" might as OTL find homes in growing industrial centers. There too, if the democratic principle is not extinguished, rising populations first of craft workers and then of more or less capitalist proletarian workers might be able to secure more or less political representation and advocacy, and thus divert more of the rising productivity toward themselves, which would slow accumulation of capitalist wealth but perhaps not check it completely, allowing for the slower accumulation of concentrated wealth permitting gradual development of centralized industrial production--but with a stronger consumer market of better off proletarians who also are politically active and see to it the law is as much on their side as on that of the more wealthy. It may be that overall, despite constricting the accumulation of capital in few aristocratic hands, that industrial progress picks up the pace on the basis of a wider population, better fed, better educated, more active, who provide essentially the same rate of innovation and invention and thus Britain does become the industrial powerhouse of OTL.
Without a strong central regime, can Britain (I am pretty much assuming that Scotland does get absorbed into an island-wide system, and leaving vague the question of how Ireland either gets absorbed or gets loose--I am in fact assuming the Irish too get absorbed in, perhaps with less overall violence and repression than OTL, perhaps with as much or more) field anything like the OTL Royal Navy? I suspect that the basic maritime bent of the coastal British people will pretty well provide for a strong merchant fleet and that the shipowners, perhaps having to contend with sailor crews more assertive of personal rights but probably recognizing the need for unified command of a vessel, be it mercantile or military, will to some degree combine arming and militia-organizing their merchant ships with specialized naval warships and at any rate mount a fairly effective Navy capable (with merchant militia support) of defending the isles themselves, and of various colonial ports, and that overseas enterprises will be perhaps quite as ruthless as they were OTL, though perhaps the famously strict discipline of the OTL RN might be somewhat relaxed and the fleet elements therefore somewhat less effective, requiring larger numbers of hulls to accomplish the same military feats as OTL, the upshot being that Brittania does not quite rule the waves with the same iron hand as OTL but at any rate British adventurers will be able to swashbuckle their way around the world and establish colonial centers of power eventually spread around the globe.
OTL, the great opportunity fueling the rise of British supremacy was seizing control of many Caribbean sugar islands, exploiting slave labor there ruthlessly, and thus laying the economic foundations for supremacy in India and elsewhere in the tropics. A major step on the road was bringing the Spanish "Empire of the Indies" to terms permitting British shipping to supply the trade in Spanish American colonial ports.
Can Commonwealth Britain composed of a federal union of hundreds of local cantons accomplish anything like that? And would the Parliament, if it could levy the taxes and supply consensus leadership strong enough to accomplish such a purpose, approve it?
Welp, I think I have strayed pretty far down this speculative road where the original foundation is hardly laid firmly in the first place, so I will leave off such details. I do suppose a certain amount of slave plantation regimes would be founded and exploited under such a regime. It is not so clear that the OTL English and Scottish stances against "Papism" would persist as long and strongly, since I suspect Cantonial England would perforce include a bunch of tracts where in fact fairly strong Catholic sentiments persist and eventually emerge openly; certainly the Netherlands set an example of toleration, as did Switzerland--if such a regime were to arise in the British isles, it would not be founded with conscious imitation of Switzerland in mind, but after it evolves and persists some decades and generations, people in both Switzerland and Britain will notice the resemblances and start thinking in terms of comparing them, and a partisan faction in favor of tolerance would gain some traction--particularly since the deal would involve reciprocal acceptance of de facto Protestant radicalism in other bailiwicks, along with development of canton zones with tolerance or acceptance of diversity in creed. Therefore provided no particular denominational faction attempts to seize control of the rest of Britain unilaterally, the question of denomination might be defused much earlier than OTL, with it established that different faiths do not necessarily involve disloyalty to the Commonwealth as a whole. (This might well be key to a different and less traumatic incorporation of Ireland into the general system of course).
Given that the British will be cutting themselves into the Caribbean and general tropical plantation trade to some degree, I suppose the foundation and growth of North American Atlantic colonies is pretty near inevitable, though perhaps they might grow more slowly than OTL. Both Virginia and Massachusetts were going concerns before the English Civil War, which is pretty much the POD here, after all. Such a radical Commonwealth might lose control of Virginia though I don't know whom any Royalist colonials would turn to to protect themselves from reconquest by the Commonwealth eventually--most European powers capable of fending off such British ventures would be Catholic after all; perhaps the Dutch, or some rising Scandinavian power, might take an interest. Ironically if the Virginian colonists do seek the protection of such Catholic monarchs as those of France or Spain, their later reconquest by a British Commonwealth that has come to terms with English and Scottish and perhaps Irish Catholics might be smoothed over by that evolution! At any rate I expect Massachusetts and New England generally would remain tied to the Commonwealth and over time, perhaps instead of half a dozen or so New England colonies, there might be dozens then hundreds of New England cantons, and these might organically gain representation in Parliament on the same basis as British cantons, excepting the practical matter that communications between their people and their MPs would be slow. But it might be enough to keep the American colonies, even if restricted to "above the Mason-Dixon Line" or even perhaps north of still Dutch New Netherlands, and spill over the mountains to contend with the French for the OTL Midwest and Great Lakes region and perhaps west and south of there. Britain, under my rather rosy pro-democratic scenario, might overall manage the same demographic explosion as OTL, and opportunity in the New World still beckon much as OTL, with the expanding mass of British settlement being pre-organized into a federal cantonial system sending larger and larger numbers of MPs to London--or perhaps devising a system of groups of cantons picking a British resident to serve as their MP as proxies, perhaps meanwhile evolving an American based clearinghouse regional parliament, initially in Boston then moving west as settlement does.
