Either ask your fishmonger to fillet the mackerel for you or fillet yourself.
Boil the new potatoes in a pan of well-salted water with the dill stalks.
Dust the fillets in the seasoned flour and shake off any excess. Heat the oil in a frying pan and add a knob of the butter. Fry the mackerel for 3 minutes on each side then remove from the pan and keep warm.
Pour away the fish-frying oil and butter. Add the rest of the butter to the pan and heat until it smells nutty. Squeeze the juice of half the lemon into the pan then pour over the fillets. Season the mackerel with salt, sprinkle over the dill and serve with the remaining half of the lemon wedges.