Dunno, but Mr Boo and I had a heated 10 minutes arguing whether Blackpool was a city or a town the other day. Wiki came to my rescue and he's now sleeping in the shed :-)
The traditional definition is a city has a cathedral, but the Queen can also bestow city status on any town regardless of there being a cathedral in it or not.
Ely was for a long time informally considered to be a "city" by virtue of being the seat of a diocese. In 1974 the status was confirmed by Royal charter and is the third smallest city in England after Wells in Somerset and the City of London.
It certainly used to be the cathedral which identified it, but Brighton & Hove is a city now, and they don't have one. Seems arbitrary now - are there benefits associated with having city status?