Hi Stephen:
Looks like the main problem would be exchanging the currency from pounds to dollars. You'd probably need to go to a bank for that.
1. Maybe the bank could wire the money. That could take care of both the conversion and the transfer. Of course you'd need the banking numbers from the seller for that.
2. You could just purchase a traveler's check and mail that. I don't know if you can specify specific amounts or not. You may have to buy different denominations that come close.
3. Here in the US we can get a bank draft (similar to a check) for any specific amount, from out bank and use it. (It's sometimes called a cashier's check). Maybe you have the same thing. Of course it would have to be converted to dollars first.
4. Here we can also send money using the post office. It's called a money order. Don't know if this works international or not.
5. Finally, you can wire money via Western Union. I presume they could do this and convert to dollars at the same time.
This is all I can think of. Hope it helps.