as i said, i actually dont know that much about medieval europe. as for "celtic art", that would be an aesthetic change and not so much an important change compared to their political, social, and military history. perhaps their renaissance could be in architecture so we have these grand, cathedral-like castles more magnificent than buckingham palace
art movements are important representatives of economics, politics, and intellectual history. the Italian Renaissance came into being because you had increasingly wealthy city states that were centers of trade and increasingly connected to the wider world. The Italians were influenced by Byzantines immensely, without that important connection to the classical era the Renaissance wouldn't be the same.
but also it comes down to the fact that if you want a britain with immense architecture and advanced art in the thirteenth century BritaIn has to be much richer than it was.
if the English platagnets win the hundreds years war, they now rule both France and England. So likely they will move the capital to Rouen in northern France which is exactly between Paris and london.
In the future England would become the lesser member of this united kingdom. the Aristocracy would be mainly French, and the major money maker would be French lands.