Peel the potatoes and cut into even-sized chunks, then cook in a large saucepan of boiling water with the lid on for 20 minutes, or until tender when pierced with a knife. Remove from the heat and drain thoroughly. Leave for 5 minutes with the lid off.
Meanwhile, in a frying pan melt the butter and add the shredded leeks. Cook for 5-6 minutes until softened and beginning to colour. Mash the potatoes then, using a wooden spoon, beat the potatoes until smooth before adding the leeks with the milk and mustard. Season to taste.