To the OP:
I am also British and have been here for a few years myself. I'm about 4/5 done with the ground school through Bristol Ground School. The ground school is pretty good for part time or distance learning but does not include any flight time or training, purely the JAA ATPL written examination material. The exams are a lot of work but depending on your flight time / type ratings / etc etc you may not have to do all or any of them (there are some exemptions listed on the Bristol website). PM me if you want any more detailed info on what and how i've been doing it!

The CPL conversion can be done over in the US at the schools others have listed above but the IR has to be completed in the JAA state that you are trying to get the ATPL from. Again, if you want any other info, PM me.

Hope this helps, it all seems extremely complex in comparison with the US / FAA.