Another option to gain legal residence status in the US is to win the greencard in the lottery.
UK citizens are not eligible for the Green card lottery.
As a pilot you can forget getting a H-1B anyway.
Not true - as long as you can prove your special skills, could be JAA licences etc and meet the other relevant requirements there should be not problem - a good immigration lawyer would help you out with that assuming you had a sponsor.
Process time is 6-12 months, but during this time, you can work in the US.
We have someone where I work who got married last year and still can't work flying over here until his green card arrives.
davepearsall - you will be wasting a huge amount of your time and an even bigger chunk of your money doing the APP at Oxford if you want to fly in the US.
Look into a degree scheme which includes the FAA rating over here - probably based on a J1 visa - if you find an employee which finds you valuable enough than an H1-B visa is probably the way forward - who should put you in touch with a relevant lawyer.
Either way you do your training if you first undertake JAA training you will have to convert to FAA, and vice versa! Most are training as required which is probably around 5-10 hours from JAA to FAA but most people for an FAA IR to JAA IR take 10 sim and 10 in the aircraft - possibly more.
Its an expensive and bureaucratic process. If I were you I would really question why you want to work in the US so much?
Good Luck.