"Criteria
City status is not, and never has been, a right which can be claimed by a town fulfilling certain conditions. The use of specific criteria could lead to a town claiming city status as of right, which in turn might devalue the honour. All applications are considered on their individual merits.
Must a city have a cathedral?
No. "
http://www.dca.gov.uk/constitution/city/citygj.htm#part2