The 2011 film “Ironclad” covers the aftermath of King John signing the document - not sure about the historical accuracy but if you like storming castles, siege engines and bloody mayhem, check it out.
‘Ironclad’ amused me when I saw it, as somebody who lived in Rochester for some years - real effort had been made to show the castle accurately (and the ruins of the castle are still a very impressive site today and show the damage caused in 1215 very clearly), but none whatsoever to show the equally large and impressive Cathedral just next door, nor the town that existed.
Good movie...and they tried to stick to true history....the pigs did happen!