I agree with both sides of the argument.
I agree with Cait et al that the docs are required for money laundering purposes, this was decided upon by the FSA and the banks are just following the rules the FSA has created. Did you know that technically the bank could come verify your address with a home visit? I studied this for my investment management certificate exam which I passed and which allows me to consult to UK clients - and I remember being very excited when I read it. Should have shown that to all the banks when I didn't have a utility bill!
However, I also agree with Paul that this money laundering reason is taken way way too far. I understand that the UK is a prime destination for money laundering and that based on the previous experiences it is an important issue. But please can we have some common sense? I think of it in relation to the ID requirements for getting on an airplane - if you don't have a passport or US drivers license/ID, you can't get on right? Well no, actually if you don't have one of these, the airlines can still let you on within reason - if they determine that it is reasonable (ie you had your wallet stolen, you are not in your home state so can't get a replacement ID, etc). But here I have encountered this blind following-of-rules that really frustrates and concerns me.... And I do feel that the govt. is on a slippery slope against protecting citizens' privacy here. But that is another issue I guess.
Hope no one was offended by this as that was not my intention - just been thinking about it lately.