On the other hand, in 3 weeks you can get a lot of flying done in the UK. The last 25 hours of my PPL was done in 2 weeks with my cross country and skills test in the UK, flying from an International Airport.
Like you, I work away and come back to the UK and fly as much as possible. If you went to a good school and told them what you wanted to do, made a lot of bookings and studied hard to get your written exams and RT exam done (is good to have these completed early and makes it easier for the flying).
I actually lived in a B&B next to my school for the time that I wanted to complete my PPL.
Cost wise it was probably more expensive, but I never know when i'm going to be home, so its very difficult to get time to sort out the US Visa's, schedule flights and sort everything out.