Cook the potatoes in boiling salted water until tender, about 15-20 mins. Meanwhile, coarsely mash the sardine in a bowl.
Mix in 3 tbsp chopped parsley and half the lemon zest and juice. Meanwhile, mix the mayonnaise and yoghurt with the remaining parsley, lemon zest and juice and some seasoning.
Drain the potatoes, then mash until smooth. Gently mix into the sardine mixture and season. Shape into 8 fat fish cakes using floured hands, then dust lightly with flour.
Heat oil in a non-stick frying pan and fry half the fish cakes for 3-4 minutes on each side until golden and crisp. Keep warm; repeat with remaining oil and fish cakes. Serve hot.