Does it ever happen that British singers use American accents when singing material of traditional British origin (as opposed to faux-American singer-songwriter stuff)? I can't think of an instance.

The nearest I can remember was a truly ghastly performance of an Eric Bogle song by Janet Russell when she used some mangled mid-Atlantic atrocity of an accent under the impression that her audience wouldn't be able to distinguish it from Australian.

American Country music is largely influenced and drerived from trad Irish ballads

...except for the 90% of it that's derived from English and Scottish ones.