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Cook the potatoes in boiling salted water until really tender. Drain and allow to steam-dry in a colander. Tip into a bowl, season and mash. Stir in the mayonnaise, tuna, sweetcorn and chives or parsley. Shape into 4 cakes and chill until cold and firm.
Dip each cake into the egg, letting the excess drip off, then coat in the breadcrumbs. Chill for 15 mins.
Heat a little of the oil in a pan and gently fry the cakes for 2-3 mins on each side until golden. You may need to do this in batches – keep warm in a low oven. Serve with extra mayonnaise and salad leaves.