As mentioned previously, you can ask if the owner can accept payment in US$.
If they can take credit cards, it will automatically convert your US$ to UKP, but be aware of international transaction fees on your credit card.
Paypal, similar. Can pay by cash (from your bank account) or credit card (if accepted) and will convert funds.
Finally, two other options. Firstly you can ask your bank for a check in foreign funds - i.e UK pounds. They should be able to do this for you, but may take some time and may have a fee associated with it. Another method is an international wire transfer where you ask your bank to wire the funds to the UK. Again, there is a fee to do this, but it is simple and fairly quick. You can tell the bank you want to send, for example, 500 UKP and they will work out the conversion from USD to the UKP.
Hope that helps.