Maybe try a search - this question is asked a lot.
The big problem is the right to work and live here. No green card, then no work. Some types of Visa may suffice for short periods of time, but realistically, without the coveted green card, any job is going to be tough to obtain. That was the case pre 9/11. Likely to be even tougher now.
As for getting twin time - I reccommend saving your cash. There are places out here that will offer 100 hrs for around $12,000. That is nearly 8,000 sterling (or whatever the Euro is). A lot of leaf certainly, but far cheaper than UK.
Nothing wrong with instructing in the UK? Probably just as tough, but you will make contacts and develop knowledge applicable for your neck of the woods?
Best of luck. Remember to have fun.