Boil the potaotes in their skins in very well-salted water. (Choose roughly similar-sized potatoes so they cook at the same rate.)
Add the milk and butter to a saucepan and heat. Add 2 tbsp of freshly grated horseradish root to the hot milk and butter then infuse with a lid on for about half an hour. Do this in a separate pan just after the potatoes have gone on, and by the time they are cooked the horseradish flavour will be fully infused.
When the potatoes are thoroughly cooked, drain them in a colander and leave them to steam until just cooked enough to handle. Then the skins are easilly peeled off with your fingers.
Break up the potatoes roughly with a fork to allow more moisture to steam off.
After a couple of minutes more steaming, the potatoes can then be sieved into the pan of bubbling hot milk and butter, or eveb cream and butter and whisk until smooth.
Taste and carefully adjust the seasoning again before serving.