Preheat oven to 200°C.
Melt the butter in a saucepan and stir in the flour. Cook for one minute, then remove from the heat and add the milk gradually, stirring well after each addition. Return to heat, season to taste with salt and black pepper and simmer, stirring often, until it thickens and is cooked.
Spread a thin layer of tomato sauce over the bottom of a 20 x 30cm ovenproof dish. Top with a layer of courgettes. Sprinkle with a little feta.
Top with a layer of the white sauce then a layer of lasagne sheets. Add another layer of courgettes and continue the process to make at least three layers of each. End with white sauce. Top with Cheddar and cook in a preheated oven for 25 minutes.