Hi Joan and welcome to GoY, what you have is probably potato scab, take a look at the link below. The potatoes are still edible but you do need to remove the scabbed bits.

http://www.planetnatural.com/pest-problem-solver/plant-disease/potato-scab/

Charlotte is a second early and a salad potato; Maris Piper is a maincrop so I would suggest that you need to leave them longer for the tops to begin to die down. As far as the scab is concerned, you could lower the ph (greater acidity), by perhaps lining the trenches or planting holes with your first couple of grass mowings.

Thanks for all three responses.
Johnny, you seem to have a thing about peach pips! I got them as tubers from a garden centre.
Jimmy, I actually grew the pots in containers and the foliage has died down together so I harvested them at the same time.
It is difficult to know whether the scab affected one type rather than the other.
Thanks for the reference, Moon.

You don't normally have to peel the whole potato - you should be able to just scrape off the scabby bits with the back of the potato peeler.

Thanks Steragram. I will try this.