I am an exception to the rule. I am, or was in my youth, a moderately competent linguist, but had the distinction at my school of being one of only three (out of 750) boys excused compulsory attendance at the school choral society practices and concerts.
The token compulsory audition involved merely singing a scale. I got only as far as mi when the music master told me he never wished to see me again.
A friend of mine who did her master's in linguistics started a business called AccentSchool. Basically, it is online tutoring (via Skype) to help people improve their English accent. However, she is not British, she is American, so I'm not sure if it would be something you're looking for.