Hi Lolabola,
I did not have any problems opening up an account with HSBC last year. I called the bank, explained who I was and my situation (spouse of UK citizen), and then asked what documents I needed to open up an account. From what I remember I had to bring:
1) 3 months of bank statements from my account in the US (I had them mailed over as they wouldn't accept a fax)
2) Passport and ILE visa copies which they made themselves
3) Hubby as a valued customer for 10+ years (he seems to think this influenced their decision to give me not only a checking account with Switch but also a Mastercard--all without a job and only being in the country a few weeks). I'm not too sure if it was his continued patronage that swayed the doors open or not.
Good luck. I would advise calling the bank ahead of time, explaining your situation, bringing hubby with you if it's his bank, and bringing in the required documents.