easiest way if you have the hours which i am not sure you have there, is do the ATP written exam at FSI in Farnborough or Paris. Use the Gleim CD and follow the instructions implicitly for two weeks. No need for books.
Then on your next recurrent do the FAA ATP and FAA recurrent Hawker checkride at the same time. It is then based on your UK licence. You will need TSA approval.
Good person for advice on FAA is Maud Duboscq at Paris FSI.
