potatoes that just wont! soften...

Don't throw out the whole meal. Just take out the potatoes as Farmor15 suggests, and either put them in the microwave or leave them out altogether and make a pastry topping instead. Seems a shame to waste the whole meal, and expensive, too.

Different varieties cook in different ways, find a variety that suits you and adapt your cooking to suit, here plenty of white varieties that don't boil down. We grow potatoes on the farm and are using "Caesar" which is similar to Piper, Piper are difficult to grow which is why they cost more. English new potatoes will soon be in so a succession of varieties will be available to complicate things.
If some are hard and some soft, varieties have been mixed maybe at the farm or shop or even your cupboard.

Some potatoes do stay hard (perhaps for the reason that Fennel says)

My mother used to call them 'pig potatoes' - ie only fit for the pigs to eat.

Potatoes which have some green in them (exposed to light instead of earthed up) sometimes stay hard when boiled.
I wouldn't eat them.

I miss golden wonders. Just saying. Sorry.

I avoid whites - they go to mush and stay hard in the middle just as you describe biker. I've found its worth spending a bit more on spuds and choosing a variety that's described as best for (whatever I'm planning)

I am another fan of Maris Pipers, but not only for roasties, or baked potatoes. As Ann says, they ‘fall’ at the top of a hat if you boil them. For mash and sliced toppings I use reds. When I do a dish that needs sliced potatoes I usually simmer them for five minutes before using them in the dish.

think they were whites ann have thrown the mixture as not time to mess as Im off to work soon..looks like a trip to Tesco when I finish.. lol ..tut..

Exactly what annsixty said. Maris pipers are ideal for home made chips, wedges or roasties. They are strange to boil/mash and seem to go watery and mushy without being actually properly cooked.

I find if I put potatoes in with other ingredients in stew/casserole they don’t cook properly so always do them separately. I wouldn’t throw out, but in the morning, fish out the uncooked potatoes and put in microwave for 5 min or so (check every minute until soft). Then you can return to pot.

I am using Maris Pipers and they turn to mush very quickly if I don't stand guard.
Which variety are you using?