The Magna Carta and the English Reformation

Here's a subject for more research: did Henry VIII's actions from 1533 to 1535 violate the Magna Carta?

King John signed the Magna Carta at Runnymede in 1215, and the first clause contains this language:

FIRST, THAT WE HAVE GRANTED TO GOD, and by this present charter have confirmed for us and our heirs in perpetuity, that the English Church shall be free, and shall have its rights undiminished, and its liberties unimpaired. That we wish this so to be observed, appears from the fact that of our own free will, before the outbreak of the present dispute between us and our barons, we granted and confirmed by charter the freedom of the Church's elections - a right reckoned to be of the greatest necessity and importance to it - and caused this to be confirmed by Pope Innocent III. This freedom we shall observe ourselves, and desire to be observed in good faith by our heirs in perpetuity.

and this guarantee is repeated at the end:

IT IS ACCORDINGLY OUR WISH AND COMMAND that the English Church shall be free, and that men in our kingdom shall have and keep all these liberties, rights, and concessions, well and peaceably in their fulness and entirety for them and their heirs, of us and our heirs, in all things and all places for ever.

Both we and the barons have sworn that all this shall be observed in good faith and without deceit. Witness the abovementioned people and many others.

Given by our hand in the meadow that is called Runnymede, between Windsor and Staines, on the fifteenth day of June in the seventeenth year of our reign.

William Cobbett thought so in the 18th century--Robert Aske thought so in the 16th.

Remember that part of the background for the Magna Carta was the dispute over the election of Stephen Langton as Archbishop of Canterbury when John wanted another candidate. Pope Innocent III excommunicated John and placed England under the Interdict. Although they started out on different sides, Langton and the Barons united to force King John to seal (not sign) the Magna Carta. And, although they started out on different sides, Pope Innocent III and King John were against the Magna Carta and the barons, because John had made England a fief of the Papacy (feudally).

It's rather confusing, really, because what did Langton mean by "the English Church shall be free"?--free from interference from the monarch/the state or free from interference from the the Pope/the universal Church? Aske and Cobbett thought the former; Tudor and Stuart interpreters, like jurist Edward Coke, thought the latter.