Tax implications are the same if you are paid in pounds, dollars or buttons. If you are liable to pay tax then you are liable.
Where you earn the money will change how much tax you have to pay, though. I would assume as you are being paid in (US?) dollars then the company that is paying you is outside of the UK, therefore it will depend on the tax agreement between the UK and the location of the company paying you.
You may also find you get a CHAPS deduction by your bank if you are paid in a foreign currency. When I was paid in Euros this was five Pounds a transaction on my account.