Boil the potatoes in salted water for 12 to 15 minutes until soft, then drain well and mash until smooth. Spread the mash in the pan to cool for 10 minutes. Getting the potatoes dry is what makes the fritters hold together.
Tip the mash into a bowl and add the chopped corned beef, onion, egg, flour, Worcestershire sauce, salt and plenty of black pepper. Mix well, mashing the corned beef through the potato so it forms a thick, workable mixture.
Shape the mixture into 8 flat rounds, about 7cm across, with wet hands. Dust each one lightly with flour and rest them on a plate for 10 minutes to firm up.
Heat the oil in a large frying pan over a medium heat. Fry the fritters in two batches for 3 to 4 minutes each side until dark golden and crisp, pressing them flat with a spatula halfway through.
Drain on kitchen paper and serve hot with baked beans, brown sauce or a fried egg on the side.