Pour the water into a shallow glass dish suitable for the salmon to sit in, add the salt and sugar and stir to dissolve. Now add the lemon and horseradish. Put the salmon in the salt solution, then leave it in the fridge for 2-3 days.
Remove the salmon from the salt solution and pat dry. Cut the salmon into thin slices with a sharp knife.
Peel the cucumber and cut in half length ways. Remove the seeds and cut into batons. place it into a non reactive tub with a lid. Add the vinegar, salt, sugar and water and stir to dissolve. Put the lid on and leave undisturbed for at least 20 minutes in the fridge.
Peel the potatoes and cut into 1cm cubes. Melt the butter in a saucepan on a medium heat. Add the potatoes and cook for 1-2 minutes on low, stirring occasionally. Now add the milk and cream, cook on low until the potatoes are just cooked through, approximately 5-8 minutes. If you find the liquid has evaporated too much add a little more milk, season with salt and pepper and finally a little lemon zest.
Place the warm potatoes in the centre of the dish, arrange a few slices of salmon on the top and finally the cucumber without too much of the pickling liquid on one side along with a few sprigs of dill, grate a little horseradish and lemon zest on the salmon. Serve immediately.