If you are a tax resident in UK, as you will be, you will be subject to income tax, national insurance and other deductions in UK, which will usually be done at source (pay-as-you-earn or PAYE). As an American citizen, you still have to file your tax return with IRS, but you can claim foreign earnings exemption of up to $92,900, so unless you earn a lot, there should be no US tax liability.
Now being paid in US$, as stated, will have currency risks - you gain, lose or stay the same, depending on how $/ÂŁ rate fluctuates, as you have to convert $ into ÂŁ to pay bills etc. Whether being on US or UK employment contract shoudn't greatly affect your tax liability, as you will be paying tax and other charges in UK in either case. Generally, it's advantageous to be on the contract in the country you work in, as your employer can remunerate you in ways that will minimise your - and their - tax liabilities, such as paying part of your salary into your pension plan, share option and so on, taking advantage of favourable tax rules that exist in UK.