There have been numerous reports of exactly this happening on bitcointalk. This thread lists several people talking about this problem: https://bitcointalk.org/index.php?topic=255174.0;topicseen. Another person also asked why this happens so regularly right here on stackexchange and received what sounds like a pretty good answer: Why so many bitcoin exchanges have their bank accounts closed and have problems establishing bank accounts?

I do not live in the UK, so I cannot speak with personal experience about UK banks' opinions about Bitcoin. But if you are interested in buying bitcoins and concerned about having your bank account closed, I would encourage you to open an account with the Internet Credit Union: https://internetcreditunion.org/ They went on record at last year's Bitcoin Conference saying that they will support Bitcoin with their Credit Union, see their presentation for more details: https://www.youtube.com/watch?v=RD6fVNGEnlI&list=PLUOP0P68GJ3BGjfqoLLnzAefk3ZzXQtJ7&index=5 Unfortunately, I don't remember where in the 34 minutes it was that they said that, but it's in there somewhere.

Their bank is based in the United States, but their signup page (https://internetcreditunion.org/form-membership-application/) says you can use a foreign passport and United States tax ID number to get an account. So if you're willing to get a tax ID number, you can get an account with them. That would be my recommendation if you're interested in buying bitcoins without having to worry about having your bank account closed.