In Britain, "city" is used for a place with a city charter from the monarch, and sometimes, unofficially, for a place with a (Protestant) cathedral, although I think this latter use is now unusual (is there anyone from Rochester or Southwell who would care to respond?). It would be unusual to call anywhere else a city, whatever its size. Reading (population 348,000) is not a city.
Very occasionally, the word "town" reflects having a charter, and there are a handful of large villages which, never having had a charter, are not towns. Near where I used to live, there were Axbridge (population 2,000), which is a town, Cheddar (population 5,800), which is a village, and Wells (population 10,500), which is a city.