Put the potato, flour and milk in a bowl and mix together just enough to combine them. You don't want to over-work the mixture or the potato cakes will be tough.
Divide the mixture into four and shape gently into cakes, again handling them as little as possible.
Heat a little oil in a frying pan over a low to medium heat and fry the potato cakes gently for about 5 minutes.
Turn over (they should be golden underneath by now) and fry for 5 minutes on the other side.
Serve with a little butter on top if you want.