Boil the potatoes for 12-15 minutes until soft, then drain well and mash until smooth. Season well and leave to cool for 10 minutes.
Flake in the drained tuna and the onion, add the mayonnaise and half the beaten egg, then mix gently. The mix should just hold together when pressed.
Shape into 8 cakes with floured hands, dipping each in the remaining egg and then the breadcrumbs to coat.
Chill the fishcakes on a plate in the fridge for 15 minutes so they firm up.
Heat the oil in a large frying pan over a medium heat and fry the fishcakes for 3-4 minutes on each side until deep golden.
Drain on kitchen paper and serve with ketchup, peas or a simple side salad.