No bank will give a UK Bitcoin company an account though that might be slowly changing. As a result of that the UK Bitcoin scene is laughable compared to other places. There are no proper exchanges and very little commerce.
If banks everywhere refused to work with exchanges then Bitcoin's usage will be vastly curtailed. It's not sexy but that's how it is. If we ever reached closed loop status then the problem goes away but there'll always be a need to interact with fiat and that means banks.
As for the original question, 2037 maybe?
Their greed will be their undoing. UK Banks will eventually be forced to recognize Bitcoin commerce just like any other fee-earning enterprise. We're at that awkward stage of Bitcoin's progress, where closed-loop hasn't happened yet, so we're forced to talk to institutions whose idea of progress is ATMs and Chip-and-PIN, which aren't really new ideas at all.
They'll either change with the times or go extinct due to their own mis-steps.