Here's a question for you all: if Britain really were this multilingual, what do you think the effects would be on politics and national identity?
I guess the lead is not so deeply buried in your title, how you think it can work out. OTL a multicultural region where several different cultural areas converged became a decentralized federation in which the subdivided, fragmented instances of these several traditions could be relied upon to come to the mutual defense of any set of these cantons, and otherwise largely agreed to a mutual pact to leave each other alone for the most part.
It seems you are trying to set up the British isles for a similar sort of federation; each component part autonomous but the group is sworn not to attack each other and to combine forces somehow to repel any foreign intervention.
That's something I think would be a good idea in general, but sadly history does not give us many instances of people being this reasonable and Switzerland has got special circumstances. The fact it is a border zone of three cultural groups (southern German, French, and northern Italian and shelters a fourth (whatever the affinities of the people speaking Romanish are, I suppose quasi-Italian but distinct enough they reject the identity) small one is not sufficient in itself; generally such areas resemble the Balkans more than Switzerland. I think the very high Alpine nature of the land has something to do with it; all the communities in the Germanic core of Switzerland were very marginal; it perhaps meant that the rate of mutual attempts at colonization was so inhibited that instead of managing to set off endless cycles of violation and vengeance, people spent time building up for that in which time inhibiting factors of mutual peaceful relations developed and they learned to bargain and negotiate. Then meanwhile their mountainous bastion meant that it was difficult for great powers to simply come in and wipe the map clean and set things up as they wished; had similar sized micro-states attempted to band against the HRE or larger peripheral principalities on other borders of it or large growing and centralizing kingdoms like France, they might have given the aggrandizing lord a good hard fight but at the end of the day been steamrollered; in their mountains, they stood a greater chance better rewarding the effort of self-defense, and meanwhile their terrain, which had some value to outsiders as lines of communication to other regions, in itself lacked the value that could be squeezed by overlords in other less forbidding regions. So--the territory was less valuable to conquer, and harder to take, and an evolving culture of cantonal autonomy and federal fraternity reinforcing each border canton's credibility at defending itself (with the help of other cantons) permitted the system to expand to its natural limits--which were, not by coincidence, the natural limits of the Alpine plateau itself.
Now I am questioning this thesis because plenty of other areas in the world, in particular that latitude in Europe, are similarly mountainous, though perhaps the fact that of all the ranges called "Alps" in Europe, Switzerland does contain the highest peaks. Clearly "Mountaineers are Free" is a generic supposition too general, or anyway with some weak relative operation that generally makes for ambiguous results, much less strongly applicable than say, "Mountaineers are Poor!" But I do think the mountainous nature of Switzerland is crucial for understanding Swiss history, and very plainly so.
Another thing about Switzerland is that despite being a huge barrier to travel, it is also a communications nexus, due to being the shortest as-the-crow-flies connection between several more hospitable and easy to traverse regions. Sometimes a conquerer, like Napoleon, finds it worth his while to invest in the effort of subduing the place because he can't be arsed to have his messengers going around it. If Switzerland were geographically and agriculturally just as it is, but way off on the side of Europe somewhere with only a handful of other regions bordering it, and those with more direct communications with each other than through it--say Switzerland were exactly where Britain is, with steep forbidding coastlines preventing the development of much of a maritime culture there--then the history would be quite different. OTL Switzerland is shaped by substantial pressure of strong and growing power blocs pressing on all sides; this helped make the obligation of mutual defense truly mutual; if Switzerland bordered on other lands only on one side, then the people of that border zone would be SOL if their neighbors in the other direction were short sighted enough to see that it would always be a matter of them coming to aid their border zone neighbors but never the other way round, and so short sighted as to fail to worry about what happens when the foreign bad guys overwhelm their border neighbors piecemeal. If the region becomes unified, it will be by a process of cultural fusion probably accelerated by the sweeping conquest of the whole thing by some invader who takes the proto-cantons one by one. Either it is unified with cultural unity, or fragmented with diversity going all the way to total independence of micro-principalities at war with each other. No multicultural federation without the cultures being tentacles of a larger invasive convergence of many invaders, then.
The British isles are not situated so as to facilitate this sort of unity by sympathy and enlightened self interest then. Nor are all of its components Swiss-marginal. Some are very easy to consolidate into larger tracts which can be ruthlessly exploited for massive gain, as the Normans did and indeed several waves of other conquerors with various degrees of post-invasion cohesion did before William.
If then plausible scenarios can be found to enable five or six very distinct cultural groups to persist in the two large and many small British Isles, without one or two of them overwhelming and deeply subjugating all the rest as happened OTL, the outcome is unlikely to be a universal voluntary federation of all of them against all outsiders, logical and sensible as such a policy would be. It makes excellent sense for six or eight British Isles kingdoms (or who knows, maybe some republics or high kings of a wooly federation of micro kings among them) to federate, with or without acknowledging one kingdom or dynasty as supreme emperor over all--maybe an elective monarchy sworn to rotate among the component realms, maybe a republican federation containing some monarchies, who knows. It would be a fine thing if all these kingdoms, several of which have mutual land borders and all of which can hurt each other by sea raiding, would seriously agree to respect established borders, leave each other alone internally, and meet pledges to provide fighting forces in the form of a common navy each realm contributes both men and funding to, and common fighting forces probably in the form of separate national ones that are accustomed to combined operations in defense of the shores of one member or another. That way the cost burden, if fairly shared, falling on each kingdom is low compared to a Continental realm of the same size in the same military tech era, and perhaps someday as with OTL England/Britain, the cost-effective Navy can, with more investment in it, become an unbeatable global power enabling the several kingdoms to share access to a huge portion of the world as an excluded economic preserve. God knows that last bit is getting way ahead of ourselves though.
That would be highly rational, but if rationality of that kind could be depended on, England and Scotland would not have been mortal and traditional enemies for a thousand years or so. Somewhere in there the "Auld Alliance" of France with Scotland against England would have switched irreversibly to a mutually profitable UK long before the 18th century. OTL that Act of Union was mainly the outcome of English hegemony, with the bitter pill for Scotland sweetened and softened by the historic predominance of a Scottish dynasty over the English throne--but note that the actual Act of Union waited until the Stuarts no longer were the recognized dynasty, and Scotland later suffered bitter tribulation with the later dynasties beating the Stuart allegiance down and out. It was pretty much the capstone of an English victory then, enabled by the seduction of the Stuart personal union tempting Scots into becoming dependent on the union they had to submit to against their wills later.
There are good reasons why the preservation of half a dozen or more separate nationalities is tricky too, of course. The expansiveness of small lordships into big ones does not leave a lot of room in islands as small as Great Britain or Ireland for many realms to remain, unless peculiar factors as in Ireland encourage that in which case they become vulnerable to piecemeal consolidation by someone outside the system--English conquest of Ireland in short. That the UK of OTL at its greatest extent could be three or maybe 4 kingdoms seems reasonable, but I think 2 or just one are more likely still.