After trying Halifax (haven't been in UK long enough) and Lloyds TSB (current visa not long enough), I was able to get a current account with Barclays easy as pie.
For now, I just have a Cash Card Account, which is very limited. In three months time, they'll run it through again to see if they can upgrade me.
The account I have now doesn't do much (no Visa debit card, just an ATM card, and no cheques; it does allow 300 GBP daily withdrawals at any ATM and direct debits/standing orders, though), but it's fine for my purposes. It's similar to the HSBC passport account, from what I can tell, only there's no monthly charge.
The woman I worked with was very nice and helpful, and I was able to do most of the application online and just had to do proof of address and identity at the branch.
