Under the Air Navigation Order 2005 it is possible for operators to lease aircraft from foreign owners for limited periods. If a dry (uncrewed, operating on the lessee's AOC) the aircraft must be exactly as certificated under CAA or JAA legislature. For a wet lease (operated and normally crewed under the lessor's AOC), the lessee must prove that the aircraft is certificated, maintained and equipped to the equivalent CAA/JAA standard. Wet leasing of N-registered aircraft in UK is very unusual; unions take a dim view of foreign labour taking UK/EU jobs. Both wet and dry leasing of foreign (non-JAA) aircraft can be very expensive for the lessee, and so the practice is not particularly common. The one area where N-registered aircraft do fairly regularly operate from a UK base is in corporate aviation.
For a US citizen to work in the UK, they must have - or acquire - the right to live and work here. Normally, that means having an EU domicile, which can be by parental lineage or by marriage. In other words, you must have UK/EU citizenship. This is similar in effect to the 'Green Card' procedure in the USA. There are, as always in these matters, exceptions and oddities, but, in general, unless you or your parents were born here, your chances aren't great. Exactly as it is if the situation were reversed.
For more - and more accurate - information, contact the immigration department of the British Embassy in Washington DC.
Scroggs