Put the vegetables in a heatproof bowl. In a saucepan, heat 110ml/4fl oz of water and all of the white wine vinegar, stirring in the sugar and salt until dissolved. Pour the vinegar mixture over the sliced vegetables and set aside to pickle for 2 hours. Drain the vegetables, discarding the pickling liquid.
Meanwhile, for the herb oil, blend all of the ingredients in a food processor until smooth. Strain through a fine sieve, then set aside.
For the dressed crab, blend the egg yolks, vinegar and mustard in a food processor until pale and creamy. With the motor still running, gradually pour in the oil in a thin stream, until the mixture forms a thick mayonnaise. (You may not need to use all of the oil.)
Put the crab meat in a small glass bowl and cover with the mayonnaise. Season, to taste, with salt and pepper. Chill in the fridge until ready to serve.
Just before serving, lay the mackerel fillets, skin-sides facing upwards, on a baking tray. Heat the skin of the mackerel all over using a chefs' blow torch, until the fish fillets are completely cooked through. Alternatively, preheat the grill to its highest setting and grill the mackerel fillets until cooked through.
Drizzle each serving plate with the herb oil. Place one mackerel fillet in the centre of each plate. Spoon half of the crab mayonnaise on one side of the fish, then spoon the pickled vegetables on the other side. Garnish with the wood sorrel and serve.