Somewhat inspired by Nek's
Astonishing the World TL in which he attempts to mix the Crimean War with the American Civil War and so forth...the late 14th century in England saw a number of upheavals aimed at the power of the Crown and the established (Catholic) Church. Most of these were essentially caused by popular dissatisfaction at either the continuation of, or at least the handling of, the Hundred Years' War.
These included the
Percy Rebellion (an early part of the Wars of the Roses), the rise of the
Lollards (proto-Protestants who attacked Catholic iconography and corruption) and the
Peasants' Revolt, which was originally a simple revolt inspired by rising taxes to fund the war, but later developed an anti-clericalist ideology and anti-noble ideology, seeking to install a state which had one king and one archbishop and then everyone else was equal citizens.
Is there any way in which we can combine these events - spread over a course of 20 years or so - into one big anti-establishment movement? Lollardy was also strongly connected with the Peasants' Revolt (persecution of Lollards really stepped up after the Revolt was defeated in OTL), so that's easy enough. The rest is more difficult, but could perhaps one of the Lancastrian claimants to the throne (and his Percy backers) have decided to enlist the help of the peasants purely on realpolitick grounds to help attack the Plantagenets, only to discover afterwards that they were now too powerful to ignore? A bit like Cromwell and the Levellers a few hundred years later.
Of course, this is not a particularly interesting WI unless we assume that this movement wins. So let's say that we have an England by ~1410 or so which has a Plantagenet king, powerful Percys who rule the North, and a watered-down form of the peasants' ideology which has resulted in the rooting out of corruption, a more independent established church and the tolerance of Lollardy. This would be expressed through a somewhat reformed Parliament, which already had significant powers by this point in OTL, and thus would be hard for the establishment to crack down on afterwards. Presumably this England would have withdrawn early from the Hundred Years' War, which is now only the Fifty Years' War or so. Now what happens?