I think if a girl is cute, she could be speaking Swahili and you wouldn’t notice. But overall, an American accent would be more of a turn-off than a turn-on in Britain. But this again is not due to the accent itself, but the political and social implications, stereotypes and assumptions. I was recently in Riga when an American boy came and joined us. He proudly announced he was from New Jersey (which we could have figured out by his accent anyway). The expression on both girls’ faces was “uh oh”. At the end of the night, one of the comments was “what did you expect from a stupid American?”.
So I think the accent itself merely denotes the origin, and then all the connotations kick in. Aussies are expected to be crude and macho, Americans to be loud and arrogant, Brits to be aristocratic and old-fashioned (even if the guy you’re talking to is some half-drunk Cockney or Geordie hooligan on his way to a brawl). And of course there are also all the foreigner accents too.
Personally I’d probably get turned off by a southern (eg Texan) accent, but would be fine with something like New York or Boston. And of course it always depends on the person. I’m sure the ladies here will agree Brad Pitt was just as sexy in “Snatch” (playing the gypsy) as he was in “Inglorious Basterds”. And the same goes for female actresses.