You only want it to say "x claims that it is part of the uncodified constitution" because you disagree with the claim and want to lessen its authority. Have you actually found a source yet which would say its not part of the uncodified constitution? I would have thought that almost everyone who accepts the existence of an uncodified constitution would accept Magna Carta is part of it. I therefore don't see the need to attribute it to one source only, especially as I don't think it's particularly controversial to say that Magna Carta is part of the uncodified constitution.
Re: John and the barons, could we have more balanced quoting, then please? At the moment it's all "the barons broke faith with John". Carpenter's quote that John had "little intention of keeping to it. Distrust between the two sides was overwhelming" would seem to provide balance to the current quotes that it was all the barons' fault.