Basically most banks within the UK are friendly to Bitcoin, I've had transactions with the name Bitcoin come up multiple times and didn't hear a single word from both Barclays and Hsbc. In fact, I even mentioned that I use it for Bitcoins to HSBC and they didn't care at all but actually asked me to tell them a few more things about Bitcoin. Further some banks on the channel island have come out and said they want bitcoin.
Does any of them open accounts for non-residents?
Hmmm that's a good question, the channel island is basically a tax haven so I would be surpised if they didn't