On the subject of naming UK (and indeed generally European) cities, one should not follow it up with the name of the country, or the name of the county etc. The idea being that, as this is the "old world", the cities (and names) here are the "original" ones and require no other qualification. The capital of Great Britain (and England) is London. That's it. Nothing else. And Cardiff, Birmingham, Athens, Paris etc require no further definition.

Subsequently built towns and cities in the New World named after those original "old world" places are differentiated by using the name of the state/county etc as appropriate.

And so, Birmingham is distinguished from Birmingham, Alabama; and Paris from Paris, Texas.

In Europe it is part of the stateside visitor's caricature that they should refer to "London, England" etc.