Unless you are in a small village, all major supermarkets have strings of cash machines, high streets have them, many but certainly not all rail stations - all the big ones do, it won't be hard. More rural areas, a bit tougher.
Is your B&B in Bath or London? If so, no probs waiting until you get there or nearly there.
I am another who has notes in wallet from years ago - I never pay cash for anything.
There was a time in the heatwave when I came out of the supermarket and a charity collector for a hospice was offering name brand ice creams (Magnums for those in the know) for a one Pound donation in the charity tin. Ooops - no change. Stayed hot - no ice cream....