The population of Wells was only circa 12,000 in 2018 and with a built-up area of just 3.244 km2 it claims to be "the smallest city in England".
Does an urbanised area have to have a cathedral to be a city?

In England: usually YES. The presence of an historic Anglican cathedral makes a town a city e.g. Chichester, Ely, Hereford, Truro, Wells, Rochester, Winchester, Salisbury, Ripon, Lichfield, Southwell, Chelmsford. None of these have particularly large populations.

This association between having a historic cathedral and being called a city was established in the early 1540s when King Henry VIII founded dioceses.

In Wales even St David’s (pop 1840) and St Asaph (pop 3350) are called cities though they are just large villages.