Aside from the more obvious associations with english writings like that of John Locke and Thomas Paine, I've seen 18th century woodcuts connecting Magna Carta to the contemporary grievances of the American war. The language used by English radical groups like the Levellers and the Diggers seem strongly related to the rhetoric of revolutionary american politics. I've even seen connections made to the 1381 revolt and the legal reforms of Alfred the Great.
How far was the American War of Independence and Revolution a continuation of (actualisation, even?) of a tradition of English dissidence and radicalism?
It is very true that there had already been quite a lot of change in the English conception of government and individual rights. That had come in the previous century. Much of it had come about as a result of the English Civil War. Before then, the king was thought to be king by divine right, and embody the state. And, really, there was not a major change in that until the 1630's. It was only as the dispute between King Charles and Parliament worsened, Parliament, desperate to find some sort of legal precedent for not being traitors to that divinely given authority, seized on the Magna Carta: before then it had previously mostly been ignored. As the Civil War progressed,and the king defeated, in the manner of other revolutions the power descended to a much lower level, in this case, the New Model Army, and there was a new conversation on how to use that power , featuring the Levellers. This was shown in the famous Putney Debates, where radicals in the Army confronted Cromwell with their new ideas of an ideal society...and Cromwell tried to pacify them,keep them in control. The Civil War and Interregnum also had many other groups than the Levellers, mostly religious schismatics. But Cromwell would manage to create something like a monarchical structure around himself, and unlike the Levellers most of those groups were ephemeral. The communal Diggers have gotten a lot of attention in modern times, but they came and went very quickly. The reason we know about so many of them is that mot of these groups eagerly made use of the printing press. A Londoner in the 1640's opening her door in the morning would often find it covered in tacked-on pamphlets, denouncing Catholics, announcing the beginning of the Fifth Monarchy described in the book of Daniel, or announcing that everyone had to take off all their clothes and go back to the garden of Eden ( the Adamites ...I think that most big social revolutions have featured people who take off their clothes and run around in the woods)
When Charles II was invited to come back to England, it was in part because people had gotten tired of the revolution. He did rule in part as a divinely-appointed king. But the precedent had been set, and when his brother James was not only disagreeably Catholic but sired a Catholic successor, he was booted out in the Glorious Revolution. That was the occasion for John Locke's musings on the rights of man, to life liberty and property. And after William died, it was the government who asked Anne to come be queen- someone very agreeably fervently protestant ( which was very important at the time, something notably missing in her portrayal in the movie *The Favorite ...*but then, most historical dramas today don't give anyone a religious life). And, when Anne died, it was the government who asked another Hanoverian, George, to come and be king.
So, yes, by the time you get the Colonies complaining about how they're being treated by the English government, that English government was much changed from what it had been in, say, in the early 1600's when the Colonies were founded. Despite the constant complaints to King George in the Declaration, they were complaining and appealing to a Parliament, not a King, and that Parliament had at least some popular representation. And it had a few voices sympathetic to the Colonists, such as John Wilkes and Francis Barre ( which is why there's a Wilkes-Barre PA). There would still be plenty of hereditary authority, plenty of Lords and Dukes- real popular representation would only come about in the next century. But King George was serving at the pleasure of the nation, not the other way round.
I forgot to say: the Putney Debates were transcribed at the time, have long been in print ( though copies have become little expensive) . They make great reading: amazingly modern-sounding discussion of why there have to be lords and not just people, why everyone can't vote. .... There's a permanent exhibition at Putney and a useful website