There are US schools which offer JAA PPL training, so in theory at least, you could qualify over there and be good to go with your hours building as soon as you got back to the UK. However, don't underestimate the differences between JAA and FAA lands - a PA28 flies the same wherever it is, but there are significant differences in RT, airspace and weather, and personally I believe it's better to lay the foundations of your future career in the place you actually plan to fly commercially.
It might be better to explore the US (or wherever) once you have the PPL, and are free to build hours and experience as you see fit. Hint - don't just fly in straight lines from one sleepy airfield to another - push yourself as much as possible during hours building - print off a copy of the CAA's CPL skill test notes and aim to fly to that level of accuracy. It's a lot cheaper than learning to do it during the CPL!
Flybe does indeed prefer applicants to do the CPL, ME & IR at one school, which gives them a clear training record and allows the recruitment people to pick the phone up and say "what do you think of so and so?" They are not bothered about the PPL or ATPL writtens (apart from the results!). I can't think of any other airlines with this policy off the top of my head - excluding BA, who as davey147 said, only take low-hours pilots from integrated schools. When they are recruiting, that is, which won't be anytime soon.
One final point - I think your timescale (2 years) is a bit optimistic. The recession is far from over, particularly in aviation, and it will be a long time before anyone starts recruiting significant numbers of 200hr CPLs. Flybe are a major player in that market, and we have quite a few cadet pilots working as cabin crew already. That situation will not change until the majors start recruiting experienced pilots, and even then it will take some time to filter down to the newly qualified guys. I'd say 3 years is looking more likely, but at least you'll give yourself that flexibility by going modular.
Best of luck.