I am originaly from Eastern Europe but I lived in England for nearly 7 years before end up in US. My accent is really mixed and sometimes it's hard for peole to figure out where I came from. I remember first when I moved in US nearly every man I met had his jaw dropped and when I stopped talking, they smile and said to me: "Please keep talking, I can not get enough of your accent". I have not met any guy who didn't like it, with woman it's opposite story of course ;)
I am not an American man, but I can tell you it's been my experience - being British and Black - that American men find me doubly attractive for my race and my British accent. I don't actually think I have that strong a British accent as I studied in the States and worked in a US stock brokerage firm for many years! But still I get the constant comments about how sexy my accent is, lol!
I have been back in the UK for nearly 5 years now, so I guess I sound more British now than ever, lol!
I was in e-mail contact with an American man I met on here who (having never heard me) really loves the British accent - very gratifying indeed.
So I guess it may be right to assume that the general consensus is that American men find the British accent attractive. British men and women find American accent super sexy too! So the accent attraction/affinity is mutual.
Can't speak for all American men, but for me the answer is definitely yes. Not sure I can answer why, but I think there is a mystique about it. The accent adds to the charm and the cultural difference than we are used to. A lot of people have never been to the UK and don't realize people are people no matter where they are (good and bad). I lived in England for 8 years and am still blown away by an attractive woman with an accent. Nothing drastic, Midlands is nice. Some people here in the states like a southern accent, others it makes no difference. I guess at the end of the day, for some people, it is a preference like any other attribute.