Gather the ingredients.
Place the potatoes in a large saucepan, cover with cold water and add a pinch of salt. Bring to the boil and cook until tender. Drain, then mash and keep to one side.
Cut the eggs in half, remove the yolks and cut the white into tiny dice. Place the yolks into a fine sieve and push through using the back of a spoon.
In a large baking bowl, add the potato, sieved egg yolks, diced egg white, parsley, horseradish or horseradish cream and a pinch of salt and pepper. Stir well.
Flake the mackerel into large chunks and add to the potato mixture, stir gently until all the ingredients are well mixed. Do not over mix or the fish will turn to mush.
Divide the fish mixture into 6. Roll each sixth into a ball, dip into the flour and roll until evenly coated. Dip the ball into the beaten egg, again roll to cover evenly, then again dip into the flour and repeat. Flatten the ball into a patty and keep to one side. Repeat with the remaining fishcake mixture.
Heat a skillet large enough to hold 3 fishcakes. Pour in enough oil to cover the bottom of the skillet, 1/4" deep. Heat until hot but not smoking.
Add 3 fishcakes. Cook for 3 minutes, flip over and cook for another 3. Remove from the pan and drain on kitchen paper. Keep warm. Repeat with the remaining 3 fishcakes.