Some good news to report! Thanks to some more great advice on my recent posts I have had a telephone conversation with Wells Fargo in London who say they can open a bank account for my wife and I despite lack of SSN. I have made an appointment for next Tuesday, 2nd, ok 2hrs on the train but a small price to pay and I will report how I get on. They need some usual forms of id, passports, driving licenses, some bank account history statements and so on but all sounds straightforward. Reminder to new readers - we are due to relocate to Florida on an L1 visa in June / July and we are attempting to get financial life underway but have had a few bumps on the way! Thanks for all the great help so far. Wells Fargo are not big players in Florida but Wachovia are and they are owned by WF.
Before I got my SSN, I opened a Wachovia account while on an M-1 visa, and a Bank of America account on a J-1 visa. I also helped a friend with a B-2 visa open a Wachovia account. A passport was sufficient each time, no SSN or ITIN. All these were in person at a US branch. I haven't tried it while on the VWP.
Re: Opening a bank account without an SSN - update
Had the meeting in London, all sounds positive, application made and waiting for the account to be opened as soon as next week. Hooray! they actually understood someone in my position (relocating L1 with no SSN).
Good news! Delighted to report after a brief application process and form filling at Wells Fargo in London on Tues - usual passport / driving license / bank statement supporting docs, I have been able to open a $ bank account. Yesterday they called me to give my account number and to inform that debit cards and pins on their way! This feels like progress at last. On relocation to the US they will simply flip our account stateside. We will be able to do all the usual banking processes including online banking and wire transfers etc. WF were delighted that I found them via this site and are considering advertising on here, they tell me they are in touch already! The service I got from WF I would highly recommend. Wells Fargo London IPB (international personal banking). Terry Bacchus is the man at WF.