Quote from LeeD:
If trading revenue warrants it, establishing a limited company may be a good option. Corporation tax (especially for small businesses) is way lower than personal income tax, many business expenses (like buying a laptop) are tax-deductible, and you don't pay VAT (UK sales tax at 17.5%) on company purchases. You'll need to make sure that any such company qualifies for taxation as separate entity both in the UK and the US though.
You need to get proper advice on this. Things may have changed since I was there a few years ago, but one person limited companies can be treated harshly by the Inland Revenue if they are deemed to be set up for the purposes of avoiding national insurance contributions. Under IR35 you can end up paying the employee's AND employer's NI contributions and be quite a bit worse off than an ordinary employee being paid a wage or salary. Not having to pay VAT on company purchases is unlikely to compensate.