Apply for your provisional now to get the process started. For the first 12 months since you entered, you can drive on your US license without restrictions, whether you hold the provisional or not. After the 12 months have elapsed (in about 2 months' time?), if you haven't obtained your full UK driving license yet, you
will have to adhere to the restrictions for learner drivers. But if you're very *very* quick, and if test dates are available, it
might be possible to get your full license in time to not be restricted.
This is the process:
1. Apply for your provisional license
here2. Start studying for the theory test (there are very good apps available for that published by TSO).
3. Book and pass your theory test:
link4. Once you have your theory pass certificate, you
can book a practical driving test, however lessons are
strongly encouraged to learn how to pass the test... it's
hard. Nothing like a US test. They're very particular. I had 6 hours of lessons over several days.
5. When you/your instructor think you're ready, book your practical driving test.
Costs:
Provisional license: £34
Theory test: £23
Practical test: £62
Lessons: Usually around £25/hour, I think?