I lived in England for about a year in 2009 - 2010 and I never had a bank account there. I was willing to open one, but a law (which probably existed to prevent fraud and laundering) made it very hard to do so without proof of permanent residence in the UK, which I did not have. Eventually I decided it was easier for me to upgrade my French Mastercard to the Gold level, where I had no extra fees when withdrawing or paying in pounds (nowadays I think you need Platinum for that).
As a French national you would only need 2 things to open a UK bank account: your French passport and some kind of document that shows you have a UK address.
Proof of address used to be easy as any utility bill would do, but now days it's trickier because so much is done online and paper bills don't get sent out much any more! And, of course, it's a problem if the bills at your house are in someone else's name. (They won't accept print outs from the Internet for obvious reasons...)
However, if you're registered for paying tax in the UK then you would certainly have a letter from Jobcentre Plus or HMRC showing your address. This would be accepted by your bank.
Another option is to get a UK driver's license, which is pretty easy and inexpensive if you already have a driver's license from your (EU) home country.
Not accepting printouts is ridiculous. It's trivial to fake a letter.
I had a similar issue when I was opening a bank account a while ago. I didn't actually get any bills in the mail, so I printed off my ISP bill, which was a pdf of what they send you in the mail. Obviously, the printer didn't fold it to fit in an envelope.
The person at the bank asked if it was a printout or actually from the mail since it didn't have any creases in it, they said they could only accept it if it was from the mail.
I told them I would just walk outside, fold it up, and walk back in, it was exactly the same as what you'd get in the mail. They ended up accepting it, even though technically they weren't meant to.
It's ridiculous, I don't actually physically receive mail from anything. All my bills etc. are done electronically, I even sign contracts electronically.
Good point - I wonder how many of those millions are non-permanent residents. The ID requirements are onerous, and like most countries it's easy to get stuck in a cyclic dependency loop of paperwork.
