Peel the potatoes, then grate them into the middle of a clean tea towel.
Grate the onion on in top, then wring the tea towel out, squeezing as much moisture as possible from the potatoes and onion. You want to be pretty tough about it, the cakes will hold together much better the less water is left in them.
Beat the egg in a mug then mix in to the shredded potato mix along with the flour & salt. Mix everything together really well.
Roughly divide the mixture into 6, and shape each portion into a patty shape. You don't want them to be more than half an inch thick.
Heat some oil or dripping in a heavy frying pan until shimmering, then carefully lay 2 or 3 patties into the oil. Leave for 3 minutes, then very carefully turn the cakes over to cook the other side. Cook for a further 3 or 4 minutes, slide out of the pan, resting briefly on kitchen paper to soak up any excess oil and serve immediately.