The biggest one for me is Guildford, since it meets so many of the traditional criteria (and is a long established centre). It has a cathedral, it has a university, and it is a major hub for its county. And the main football club is even called "City"!
You could also apply a very similar logic to Reading (it doesn't have a cathedral but AIUI that was because the Abbey meant no-one thought there was any need for another major ecclesiastical hub). Other county hubs which are big historic places like Northampton and Bedford also have fairly good claims in my view, though sadly Milton Keynes influencing the region and swiping a lot of the shops and influence probably means neither will get it (especially now MK is a bona fide city).
I'd also have some left field picks. Newport on the Isle of Wight very distinctly feels like a city - a small one, but a city. The place feels far more important than you'd think based on population alone (as the main hub for the Island). Dumfries is such an important and undisputed regional centre (even if a little faded) that I was genuinely surprised that they picked Dunfermline over it for Scotland's 8th city. And finally, on a very different note, I'd like to see another London borough promoted to city - either Southwark because of how integral it is to South London's history and identity, or Croydon because it is a somewhat semi-detached centre of its own (more so than anywhere else in London IMO) with a population greater than most actual cities and a skyline to match.