There's not much work in the U.S. right now. You might have been better off staying in the U.K. and going on the dole while you sought work. It's a lot harder to get on welfare here (our equivalent of the dole) than there, from what I've heard.
I'd say, first of all, drop your standards and expectations. Don't limit yourself to looking for jobs you want, or jobs you have experience with. Be willing to accept minimum wage, and find a way to live on it. In other words, if you've been paying $1000+ for an apartment in New York, you've got to find some way to quit doing that. I don't know how, and I don't know what the heck New Yorkers do, but you'll have to. It's a horribly expensive way to live, and it's not feasible unless you have a *good* job.
First of all, try to get on some kind of welfare program. Your situation might be desperate enough that you qualify. It's worth a shot.
It might be cheaper to use UPS Mailbox service (an improved P.O. Box) as your "permanent mailing address," and free yourself up to sleep wherever you can find. If you're bad off enough, you might need to get a gym membership with a gym that has a shower and a locker as well, so you can store your essential belongings and shower after you've slept in the street (though I'd think surely someone out there would be willing to help so you wouldn't have to). In this case, you'll want to get library memberships so you can do research online, in the newspapers and such, etc. The biggest priority is making sure you have access to a shower and a change of clothes. That's actually more important than having a safe place to sleep, or even food (it's water you can't live without, and water is free) despite what your instincts might tell you, because that's what you need to get hired.
New York is an unreasonably expensive place to live, from what I've read. There's not an apartment there that costs less than $1000, not even a cockroach-infested one that's been horribly maintained. It's too bad you didn't come to a cheaper area that wouldn't have eaten your money so quickly.
Good luck. Humanity is a completely unfair and screwed up thing during bad economic times. They force and hold you backwards, prevent you from getting ahead. I personally think the people who already have jobs and experience have used their positions to conspire to keep new workers from entering the workforce.