If that is all you want it for, it should be relatively simple.

If you want a plain old bank account, all you have to do is get a Social Security number. Non-resident numbers are available from the Social Security Administration for precisely this purpose. You may be able to get one by mail, however the people I know who have gotten them have gotten them straight from SS offices.

Better yet, most US brokerages offer different types of "One" accounts specifically geared towards stock transactions. These accounts basically allow you to buy/sell securities and they give you a check card and debit card for accessing your funds. Better yet, if you are not a US resident, they will have you fill out a form stating so, so that you do not need to get hit by taxes.

And no, you do not need a US address for either of these options (although I could imagine that some US banking people would be confused about the whole thing and tell you otherwise).

I would suggest either Charles Schwab for the "one" account, and either Citi or Chase for a regular account.

Another option is that any of these institutions listed above may allow you to maintain a dollar account out of London.