(2-part post):
Stoke-on-Trent is major city. It's population is around a quarter of a million people (which is roughly the same size as Sheffield or about half the size of Edinburgh), so I think that there's a reasonable chance that you might find a branch of Boots ;-)
(Actually, there are at least 5 branches)
However, if you try to find 'Stoke-on-Trent city centre', you'll find that it doesn't really exist (even though the link provided by Cazzzz1975 refers to it!). That's because Stoke-on-Trent is actually made up of 5 (or 6) separate towns. It was originally formed by joining Hanley, Stoke, Burslem, Tunstall and Longton together to form a single city. (Stoke is often called 'the city of 5 towns'). At the time the city was formed, Fenton was just a village within its boundaries but it now forms a 6th town.