Preheat the oven to 200C/390F/Gas 6.
Cut the monkfish into chunks and then dredge in the seasoned flour.
Melt the butter in a large ovenproof frying pan and, when foaming, add the fish. Fry for a couple of minutes on each side, until browned.
Squeeze the lemon juice over the fish, and move the fish to one side of the pan.
Add the potatoes to the pan and cook for two minutes.
Add the cherry tomatoes and cook for a further two minutes.
Finally add the artichoke hearts to the pan and season, to taste, with salt and freshly ground black pepper.
Distribute the potatoes and fish evenly in the pan, then transfer to the oven and cook for 3-4 minutes, or until the monkfish is cooked through.
To serve, place the fish and potatoes onto a warm plate. Squeeze the remaining lemon over and garnish with fresh parsley.