Preheat the oven to gas 4, 180°C, fan 160°C. Flake the mackerel and pop into a bowl.
Squeeze the moisture out of the grated potatoes and add to the mackerel, along with the egg. Add the thyme and some pepper (but no salt as mackerel is salty enough) and work the mixture with your hands. Make 8 cakes and dib them in the breadcrumbs to coat.
Oil a baking tray and pop the fishcakes in and bake for 20 minutes, gently flipping them half way through.
Meanwhile, blanch the beans in boiling water for 3 minutes and drain.
Toss with the olive oil and garlic, and sprinkle with the feta and pomegranate seeds. Serve with the fishcakes.