Levelling Up
Levellers engage in slightly smarter politics in 1648-1649. They are not quite as loud in their condemnations of the established order, less mutinous, and generally focus more on surviving and retaining some influence rather than taking more aggressive stances. They avoid being quite so purged as in OTL, and continue to be a prominent force in national politics, particularly in London and in the ranks of the New Model Army.
In April 1649, a group that would come to be called the Diggers settled on Crown Lands, essentially the former domain of the king, and now the unused property of the Parliamentary government. Local landowners complained to parliament, worried about the precedent commoners claiming land for themselves would set. Thomas Fairfax visits the group, and noting the significant Leveller sentiment in favor of the Diggers in the army, opts not to intervene. This is the same as OTL, but here because of increased Leveller interest he goes slightly farther, explicitly endorsing the right of Diggers to settle on crown lands, instead of leaving it to a local court dominated by the local landowning class who inevitably ruled against the Diggers in OTL. Indeed, the Diggers are even assured of some level of legal recourse to the ferocious ongoing harassment from nearby landowners. Harassment of various kinds continues, but at a sufficiently lower rate that it is not able to drive the Diggers out.
So the Diggers survive, and their prolific advocate Gerrard Wistanley spreads the word of their activities. Hearing of this, common people around England begin to follower the Digger example, and occupy the unused common land in their areas. Between the Leveller influence in the army and on the streets, and the productivity gains resulting from putting additional land under cultivation by people who would otherwise be destitute, parliament is persuaded to tolerate the spreading Digger phenomenon. As the movement grows many of the more conservative MP's will begin to rethink this toleration, but that same growth makes any efforts in that direction harder as time goes on.
This status quo survives until 1653, when as IOTL an increasingly frustrated Oliver Cromwell dissolves the Rump Parliament and has himself declared Lord Protector, and king in all but name. However, unlike OTL, he has been surrounded by Leveller officers for the past few years, and had some experience with Digger communities in the countryside. With this increased confidence that the common people would back democratic reform rather than a return to monarchy, Cromwell gives in to the one central Leveller demand: a parliamentary election held under universal suffrage (well, males 21 and older).
This election would prove transformational. Cromwell would of course retain the whip hand, through his control of the New Model Army, but for the first time there would be some opportunity for common people to gain some level of institutional power. The 460 seats broke down roughly as follows: 160 royalists, 140 Republicans, 90 Levellers, and 70 Diggers. These are very rough categories of course, because no political parties were involved in the election, and few knew which of a candidate's beliefs or policies would be relevant in the turbulent times ahead. So people simply got together, picked a well liked and competent local, and hoped for the best.
What resulted was a motley assortment of 460 representatives from across England and Wales, and was both immensely flawed and the most representative expression of the popular will in English history. Representatives ranged from communally chosen representatives of Digger communities, to bought and paid for representatives of rural landowners, and from dyed in the wool Republicans to staunch Monarchists.
However, Cromwell ultimately found it to be a parliament he could work with. They were largely of a similar mind to Cromwell in that they preferred some peaceful and reasonable resolution to the chaos of the last years, even a compromised one, to continued turmoil. Cromwell remained Lord Protector, with authority over the army and a variety of entrenched powers that basically came down to him having the ability to overrule or at least block parliament on most issues if necessary, but was largely content to leave non-military matters to them. Parliament was easily convinced to enact Cromwell's first peacemaking priority: a permanent religious settlement based on religious toleration. Edicts for official religious toleration were issued, with the church essentially given over to its members as local elections for clergy became the norm. A thousand weird sects bloomed, but the mainstream English public generally tended towards a sort of bland ecumenism, with a focus on competent church government over theology when it came to choosing their local ministers. The church structure above the local parish level was disbanded, and many valuable church properties seized by the state or given over to Digger settlers.
The stage was set for the unique transitional period that would last for another six years and mark England's transition from Kingdom to Republic: the Protectorate.