Scrub the potatoes and chop them into bite-size pieces. Tip into a pan and cover with cold water. Sprinkle in a generous pinch of salt, cover and bring to the boil. Reduce to a simmer and cook for 20 mins, till just tender.
While the potatoes start to cook, finely grate the zest from the lemon and set aside for later. Chop the leaves off the radishes. Rinse the radishes and shake them dry. Use a sharp knife to finely slice them on an angle, then pop into a bowl. Squeeze over the juice of half the lemon. Season lightly with salt and pepper and toss together. Set aside.
Spoon 4 tbsp crème fraîche into a small bowl. Finely chop the tarragon leaves and the dill, fronds and stalks, and stir them in, along with the reserved lemon zest and a pinch of black pepper.
Pick the leaves from the sea purslane, making sure to discard any tough stalks. When the potatoes have about 1 min of cooking time remaining, add the purslane to the pan and simmer. Drain everything well and tip back into the pan. Stir in the butter to coat the potatoes. Cover with a lid to keep the spuds warm and set aside.
Pour 1 tbsp olive oil into a frying pan and bring to a high heat. Season the mackerel fillets all over, then lay them skin-side down in the hot pan. Fry for 2-3 mins, flip over using a fish slice or spatula, and cook for a further 1 min. While the fish cooks, tear up the parsley into rough pieces.
Pop the crispy mackerel fillets on 2 warm plates next to a pile of the buttery potatoes and purslane. Scatter over the pink, lightly pickled radishes and torn parsley. Serve with dollops of herby crème fraîche and wedges of the remaining lemon.