Awkward.
My own local bank branch is about to close, which I haven't needed to visit but twice in the last ten years, once to pay in a real hardcopy cheque (remember them?) and once to surrender my expired Secure Key (the gadget for generating one-time PINs) for secure disposal. Nearest surviving branches are both an hour away by bus: at least I'm still mobile, and as a gentleman of leisure, time is the one thing I have in abundance.

The last resort will be to take my custom to another bank. I imagine though that this would be a bit of a hassle, as several bodies individual or corporate will need to be told, and I'm bound to forget someone.