If there are no fees then I would look at the exchange rate. There is a percentage markup the bank adds to the exchange rate. Note that nobody ever gets the actual exchange rate, there is always a markup and it will vary from place to place.
I have used
www.xe.com to transfer money several times. They can take it electronically out of your US account and electronically deposit it into a UK account. There are no fees, just the markup, which they claim is one of the lowest because they perform bulk transactions all the time. It is free to create an account, but there is some identity checking because of Federal regulations regarding money laundering, etc.
The nice thing about xe.com is that you know the exchange rate you will get before committing to the transfer. I don't think a regular bank can/will do that. You can directly compare it to the real time actual exchange rate to see exactly what you are paying for the transfer.
If someone has found a better way than xe.com then I would be interested to know as I'm always looking for the best way as well.
Andy