The Google Books Ngram Viewer shows a jolly mix of "tap r", "flap r", "tapped r", "flapped r" for that sound.
My linguistic dictionaries say some phoneticians distinguish between a tap and a flap, but it seems too technical for here.
The words given by will (better, gotta, somebody...) are all good examples of taps/flaps in American English, but—back to will's original question—
I've never heard of the tflapp(ed) /t/ and /d/ having a place in the British Isles. Is there a well-kept secret in Wales?