Oh, yes, of course... the shameless tarts are taken in by anything foreign and especially so if they believe the foereigner to be intelligent. To them, something about a proper English (how do you say, "cut glass"?) accent leads them to believe the speaker to have superior intelligence... little do they know!
Andy is spot on, except that not only is the English accent not a novelty in NY, but can actually work against you. Typical New Yorkers tend to be a healthy bunch who appreciate drive and wealth, often when they hear your accent they think, hmmmnn British, must have a drink problem. Ridiculous generalising I know!
If you are going off the beaten path be prepared to repeat what you say a lot! Once to establish you are not local,twice to establish you are not American, and if you are luck the third time you might get what you want!God bless Missouri and Kansas.
I was in Louisville, Kentucky last year and people kept asking my friend if I really was English, they were so blown away by my accent! My friend said that all these people in the shops I'd just been in would be rushing home to say that they'd met an English person that day! Having said that, Louisville is not really on the tourist trail (apart from the Kentucky Derby), so yes, I would say if you are going somewhere other than the usual English destinations than you may find yourself the centre of attention!
One of the problems faced by those with a pronounced English accent, however, is the American's trying to decide whether it's English or Australian, never mind New Zealand Case in point and in line with henneth's observation is a nation wide television ad campaign for Geico auto insurance here in the U.S.. The spokesman (thing) is a gecko (get it?) lizard... the little blighter (see how quickly we pick up the lingo?) has an accent that most of the time sounds very English but also sounds likely to be Australian. No one ever wonders why any accent is used at all rather than American. I think it's to stay away from all the regional accents here in the U.S. and besides, English makes you pay attention to determine what he's talking about. Pretty effective campaign, I'd say...
I don't know if you recall that the Geico ads used a more Ralph Fiennes type of voice last year then switched to something like a voice out of an East End Guy Richie movie "it's pie wiv chips, for free"