Wash the potatoes then, leaving the skins on, cut them into cubes (about 2cm square).
In a stock pot, add some water and heat. Crumble in the stock cubes until dissolved. Add the potatoes and top up with water so that the potatoes are about 2 inches under the water level. Bring to the boil. Once it has reached a boil, turn down the heat.
Wash the leaks and dry. Cut along the length of the leek, leaving the bulb intact. Cut into slices.
Add the leek to the pot and simmer for 20 minutes.
Once simmered, pour in the single cream (or substitute), stirring while doing so.
Mix some cornflour with cold water and add, a little at a time, the cornflour mixture to the pot, continuously stirring as you go, until you reach the desired thickness.
Add salt and pepper to taste. You can add a knob or two of butter for a buttery, creamy taste.
I prefer mine without butter by my children love the buttery taste, so I pour my serving out first, then add the butter.