Hei, do I leave the courgette and runner bean plants to die and rot in the ground when they have finished fruiting or do you dig them out?
Stick them on the compost heap. You can leave bean roots to rot in the ground.
If you get a very mild winter beans are perennial and might regrow, but usually the frost gets them.
Or do what B&Q in York do and offer them for sale at half price lol