Citibank in the UK offer a US dollar checking account with cheques that clear in New York as well as a $ ATM card.

I use this to pay those few US organisations who don't take plastic money.

No charges for cheques, deposits or ATM withdrawals from Citibank machines (but expect to pay $1-2 for use of other banks' machines).

Downside: you need to have £2,000/$3,000 in your banking relationship (i.e. all accounts) at the end of the month to avoid a $15 account charge. Also no interest on this account so you would need to have a savings account for that.

Depending on your circumstances, this could be useful as you don't need a SSN.