Lay the fish fillets in a single layer in a glass dish. Mix together the oil and lemon juice and sprinkle over. Cover with clear film (plastic wrap) and marinate in the refrigerator for 1 hour.
Melt the butter in a pan and gently fry the mushrooms for 5 minutes, until tender and all the juices have evaporated. Stir in the chopped anchovies, thyme, salt and pepp