I don't grow potatoes anymore because of the blight which originated from a neighbour's plot but it sounds to me as though you have infected plants. With all the wet weather there has been in UK I'm not surprised. Unfortunately the blight is spread by the air and can spread easily to other crops like tomatoes, peppers, aubergines, squashes and melons if they are nearby. Having an Irish family I know all about the blight but, if my ancestors had left their spuds in the ground to mature instead of digging them all up and throwing them away, a lot would have survived the famine. So, you can cut off the foliage if the blight goes mad and leave the spuds to mature and then eat them - although they do not store well.
It is important to cut off the infected parts of the plant when they are thoroughly dry i.e. not on a damp or wet day or if dew is still on them. This is because the infection can transfer onto your clothing etc and you will transport it elsewhere. When you cut off the infected parts, take them a long way off to destroy them. Never put them, nor the potatoes, in your compost. It's best not to put even bought potato peelings in compost as they could be carrying the disease.
You may be lucky and be able to salvage your plants by spraying with fungicide. The sooner you start on uninfected foliage the more chance you have of saving them. You will have to do this almost daily or at least twice a week minimum to fight the blight as all new foliage has to be sprayed and when the plants are growing well you can almost see them producing new growth as you stand there.
To avoid blight in the future, don't plant any of the susceptible plants in the same plot of ground and if possible protect outside potatoes and tomatoes from rain. There are neat contraptions these days for doing so - like poles with umbrellas on top - or grow tomatoes, peppers etc under cover altogether as I now do without problems. Never water from above - a drip system is best - or old plastic bottles with the ends cut off and sunk into the ground beside the plants can be filled with water and feed when needed. Make sure the plants outside get wind around their stems - this sounds crazy since the blight is carried on the wind but it keeps the bottoms of the plants aired and it helps to cut off the bottom leaves so they are not touching the ground.
I'm really sorry if your potatoes are infected. Have a look around your neighbours to see if anyone else is infected then perhaps you can see the source. All is not lost though. You can still have some potatoes with some luck and you may even halt the blight altogether with fungicide. I know home grown taste like no other but when you see the amount of work involved - and the heartache sometimes - it is a wonder any of us carry on with it.
Crikey - this is a long reply - sorry....