AHC: Switch British and Polish Governments

Okay, the titles a bit vague, but what I'm wondering is if it's plausible to switch the development of government in Great Britain and the Polish Commonwealth? That is, have Great Britain end up with an utterly non-functional system of government held to ransom by various provincial interests and with the occasional noble uprising or civil being rather unexpected (being a de facto client of a nearby power is optional) while Poland ends up being a relatively democratic constitutional monarchy with neutered nobility and a powerful commercial class.

Lets say a POD after the Magna Carta and have this achieved by the OTL first war of Partition.

So yeah, any idea's?
 
My favourite way would be to have Piast dynasty rule longer - Casimir III has a son who continues his father policy, etc. Casimir supported towns and took care of peasants, so he didn't have to rely on knights only. With time Poland, allied with Lithuania (but not united) returns to Baltic after defeating the Teutonic Order. So Piast dynasty rules, Polish towns, merchants and craftsmen get richer and gain more influence. Eventually, Poland is slowly transformed into a constitutional monarchy.
Meanwhile in England the War of Roses goes worse and pretendents pay the knights for support with privileges. Eventually England is ruled more by cast of barons, than by the king, whose power is significantly limited.
 
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