There are five cities in the UK without railway stations (approx population in brackets):
Ripon (16700), North Yorkshire
Armagh (14800), Northern Ireland
Wells (12000), Somerset
St Asaph (3500), Denbighshire
St Davids (1800), Pembrokeshire
Although despite their city status, they are effectively little more than small towns (or even villages in the case of the latter two) with cathedrals. FUN FACT: St Davids, owing to its size combined with its remoteness, is the only British city that has never had a railway station in the first place, even pre-Beeching!