Yes - the traditional liberties of the City are long-standing and fought for. I'm not sure that being mentioned by name in Magna Carta was reason enough to leave it unreformed. The Cinque Ports have been reduced to essentially ceremonial status despite their mention (and the large majority of Magna Carta has simply been repealed over the years[0] - it's not a constitutional document in the sense that it's ever been entrenched).

[0]: https://www.legislation.gov.uk/aep/Edw1cc1929/25/9