It's is quite straight forward for someone in your position to open a UK bank account. But you do need to talk to a bank that knows what it's doing. I'm afraid your average High Street branch isn't going to have the expertise. But I can vouch for 2 banks that are well used to handling situations like yours:

Barclays International

HSBC International

They can also advise on whether on-shore or off-shore suit you best and help with tax advice.