They will take on UK pilots, however it comes down to the immigration thing. Look for a chick whilst training and hope she says yes when you ask her to marry you seems the only option.
Expect a different route to the jets compared to JAA land. You wont find many in the right seat of a 737 with 250 hours
Likely route that I know a couple of guys have taken is instruct to about a 1000 hours, with some aerial work, banner towing in between. They then moved onto light freight, google Ameriflight and you'll see the type of outfit I'm refering to. Then onto the regionals with at least a 1000 hours and 100 multi time. First post being a Dash 8 or CRJ/ERJ etc.