I ran into a similar issue booking a Swiss mountain hotel years ago. From a US account, just look into an international wire transfer. They should have an IBAN number, which is a standard account number to send to. It's the same thing.
If your bank won't do an international wire, you can sign up with a foreign exchange company like OFX to do it. You may find more hassle in this, since you are sending to someone other than yourself. (they are very sensitive to fraud) This may take more time than from your home bank. It may be a lot cheaper, though, too: $35 is a pretty standard bank fee for this.
You don't really need a UK account; really, anyplace other than the US, and this would be fairly routine. It's kind of like the metric system, but for bank accounts. I say this, but for a US citizen or permanent resident, foreign accounts can be a hassle.