Preheat the oven to 190C/gas 5/fan 170C. Peel and thinly slice the potatoes and put immediately into a bowl of cold water. Using some of the butter, liberally grease a 20-23cm cake tin (not loosebottomed).
Drain the potato slices and dry thoroughly in a tea towel. Place the potato slices in circles in a layer in the base of the tin, overlapping them as you go. Season with salt and freshly ground black pepper and dot with a few small pieces of butter. Keep layering the slices evenly, seasoning and dotting with butter as you go. Finish with butter, season, then cover with a circle of buttered greaseproof paper.
Bake for 1½ hours, or until the potatoes are tender when pierced with the tip of a knife.
Leave to cool in the tin for 5 minutes, then invert on to a serving plate. Brown briefly under a hot grill if the top needs more browning. Serve cut into wedges.