Boil them a lot more gently, tipping away almost all of the water when they're about half cooked and letting them finish cooking in the residual heat from the remaining water & steam. Or just steam them in a steamer. Next year you could choose to grow "waxy" potatoes instead of the "floury" ones you presumably grew this year.

Didn't you ask this yesterday? I answered an identical question then with a pretty similar answer anyway.

This is James 1964's only question so far Stera. Must have been someone else with the same problem.

Found it! Tony-something-or-other asked
http://www.growsonyou.com/question/show/60692

My freshly dug* potatoes cook faster than shop bought potatoes. Not just boiling, they roast quicker as well. I do not peel potatoes maybe that is why mine don't mush. I also think 10 mins is all it takes.

*Tipped up Hessian grow sack.

You can also solve the problem by steaming rather than boiling your potatoes. Flowery potatoes will always need watching like a hawk when cooking as they can go to mush in no time try growing waxy ones instead.