Pour the stock into a largish saucepan with the diced potatoes and bring them to the boil; then cover and simmer gently until the potatoes are soft – that should be in about 10 minutes.
While this is happening, start to prepare the vegetables: first the leeks which should be slit open lengthways and then cut across in 5mm slices. Wash them in several changes of water to get rid of the dirt, then drain in a colander. Now take a sharp knife and peel and dice the root vegetables into quite small pieces, and cut up the celery too. The chopped bacon should be fried without any additional fat until it’s fairly crisp.
Then, as soon as the potatoes are soft, rub them through a sieve (or liquidise them) and return them to the saucepan together with the vegetables, bacon and any fat that came out of it. Now bring the soup up to a gentle simmer, taste and add some seasoning, then cover and cook gently for about an hour. The frankfurters should be sliced thinly and stirred into the soup to heat through gently just a few minutes before you are ready to eat.
Serve it very hot.