To make the beurre blanc, place the shallots into a saucepan together with the wine vinegar, lemon juice and white wine. Bring to the boil and reduce the liquid to about a tablespoon. Add 1 tablespoon of cold water, and keep on the heat to reduce the liquid again to just a tablespoon.
Turn the heat down and over a low heat, whisk in the butter about 25g at a time. The sauce will emulsify. Once all the butter has been added, remove the pan from the heat and pass the sauce through a sieve into another saucepan. Set aside until needed, but do not refrigerate or the sauce will separate.
To cook the sea trout, heat a frying pan over a medium heat, add a good splash of rapeseed oil and the butter. When the butter foams place the fillets in the pan, season, press down firmly on the fillets and fry for 3 to 4 minutes. Turn the fish over and fry for a further 30 seconds, again seasoning with salt and freshly ground black pepper as you do so.
To cook the samphire, bring a pan of unsalted water to the boil, throw in the samphire and cook for 3 minutes. Drain thoroughly, smother with butter and season with salt and freshly ground black pepper.
Just before serving reheat the beurre blanc, carefully stirring the sauce over a low heat, stir in the lemon zest and check the seasoning.
Serve the sea trout on a bed of buttered samphire with the lemon beurre blanc.