You'll spend more money doing that in the US than if you do FAA Private, Instrument, Commercial & Multi then convert to JAA (f)ATPL.
You will save money on the Night Rating and IMC - they don't exist in the US. You would also save money by reducing the number of JAA written tests as you 'only' have to do writtens for the JAA ATPL. FAA Written tests are much different - One each for Private, Instrument, Commercial, Flight Instructor, Flight Instructor Instrument, and only cost $80 - $90 each.
The FAA to JAA Instrument Rating conversion is fairly striaght forward - Written Exams, and 15 hours of training, and as you appear to know find an FTO with a FNTP 2, you'll save money in the UK.
Look into the fees involved with JAA Checkrides, you'll find they equate to about $1200 per check ride. FAA fees run between $250 to $400 per checkride. Also, JAA Schools (in the US) will charge a lot more than an FAA only school - due to JAA Approval process etc.
Due to the weak dollar, it is a great time to do flight training in the US, even if you intend to use it in Europe. Also it could prove to be advantageous to have FAA certificates in Europe, as for example, a lot of Corporate airplanes are N-reg, and based in Europe.