Wash the potatoes thoroughly and cook in boiling water covered with skin for 15-20 minutes. Drain, rinse with cold water and let cool.
Stone and halve the olives. Finely chop capers. Mix vinegar, mustard, salt, pepper and sugar. Fold in the oil. Cut potatoes in half. Mix the potatoes, olives, capers and dressing and leave to stand for about 30 minutes.
Wash the cucumber, peel it in strips and cut it into large pieces. Dill wash, shake dry, pluck off the flags and chop. Spread the flour on a flat plate. Wash fish, dab dry and cut into 8 equal pieces. Season with salt and turn in flour.
Heat butter in a large frying pan. Fry the fish pieces on each side for 3-4 minutes, remove them and keep them covered and warm.
Fry the cucumber pieces in the frying fat while turning for approx. 4 minutes. Season with salt and pepper, mix in dill. Arrange fish with cucumber vegetables, chips and lemon wedges. Serve with potato salad.