The audio on https://en.wiktionary.org/wiki/Worcester and https://en.wiktionary.org/wiki/Worcestershire is correct (it says it's American, but it's the same in British).

Leicester (in Leicestershire) is a larger English city with the "-cester" suffix, meaning a Roman fort. The name is used in the US as a personal or family name: Lester.

Where the pronunciation is "ch", it's also spelt that way, as in Manchester.