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Steam the potatoes for 15-20 mins, either using a steamer basket or a simple metal colander over a pan of boiling water, with a lid on top. Put 3 plates in a low oven to warm.
Slash the fish skin a few times, then season generously and sprinkle with the cayenne. Put a heavy-based frying pan over a medium heat, adding the oil once the pan is hot. Cook the fish, skin-side down, for 6 mins, until the skin is golden and crisp. Avoid the urge to move it about.
Season the fish on the upper side, then carefully turn the fillets using a fish slice or spatula. Cook for 2 mins more until the fish has changed from dark to pale pink all over, with a little blush remaining in the thickest part. Transfer to a warm plate. Wipe out the pan with kitchen paper.
Scatter the samphire over the cooked potatoes, return the lid and steam for 2-3 mins until just tender.
Melt the butter in the frying pan and sizzle the shallot for 1 min. Splash in the wine, boil to reduce by half, then add the shrimps, tarragon and lemon juice to taste. Swirl the pan off the heat to melt the potted shrimp butter and make a buttery sauce, then season to taste. Spoon the veg onto warm plates, drizzle with a little sauce, then top with the fish, the rest of the sauce and the shrimps.