Bring the smoked water, salt and sugar to the boil, let cool then brine the mackerel fillets for 6 minutes. Pat dry then slice into small pieces.
Blend all the ingredients for the nasturtium puree together, pass through a chinois and season with salt.
Whisk all the lemon gel ingredients together in a pan and bring to the boil, pour into a container and leave to set to a firm jelly. Blend until smooth and pass through a chinois.
To finish, cut the radishes and apple into discs with a one-pound size pastry cutter. Season the mackerel with salt, dashi vinegar and lemon oil. Spoon the nasturtium puree onto the plate, sit a spoonful of the mackerel mixture on top. Dress the slices of radish and apple over the top of the mackerel with dots of lemon gel, nasturtium leaves and sea purslane.