As above, I believe that no UK bank will charge you for using one of its ATMs. There are some ATMs not operated by banks that will charge a fee, but they must warn you before dispensing any money. But that won't be an issue if you stick with the "high-street" banks.
Your own bank will, of course, charge a commission for withdrawing foreign currency, and it may also charge a fee for using an ATM that is not one of its own.
It is likely, therefore, that all bank ATMs will incur the same cost to you unless you do find one that has some sort of arrangement with your US bank - I guess the easiest way to find that out will be to ask the bank.