Shakespeare doesn’t mention Magna Carta in King John, which is about the king’s legitimacy, not his barons’ rights.
King John in music? I can only think of the King John overture (1941) by Castelnuovo-Tedesco, one of many that he wrote on Shakespearean themes. It takes as its motto the final words in the play, uttered by Philip the Bastard:
“This England never did, nor never shall,
Lie at the proud foot of a conqueror,
But when it first did help to wound itself.
Now these her princes are come home again,
Come the three corners of the world in arms,
And we shall shock them: Nought shall make us rue,
If England to itself do rest but true.”
Patriotic music for 1941, perhaps, but not at the level of Walton’s for Henry V of three years later. Shakespeare also wrote the greater play three years later.
Below, conducted by its dedicatee John Barbirolli, with the New York Philharmonic, presumably its premiere (unsearchable on YouTube because said to be by “traditional”). Vaughan Williams dedicated an orchestral Flourish for Glorious John to Barbirolli in 1957, but that term of endearment does not refer to anyone in Shakespeare, but to Walter Scott’s epithet for Dryden in The Pirate.