I have a Barclays account here and my ex has a local credit union back in the US. We arranged for him to transfer me some money and it was super easy.
I had to get an IBAN and SWIFT number for him (admittedly, a long wait on the phone because I didn't want to walk over to the branch), and some other basic information.
The best part -- the exchange rate was good, and they only charged a flat fee of £6!
Since it went straight into my account (available immediately), I don't have to mess around with transferring anything from a third-party bank.