Powdery mildew, most likely... a fungal infection common to zucchini (your courgettes), cucumbers, squash and other wide leaf varieties of vegetables. Caused by warm, dry weather.
It can be treated with some fungicides, but one has to apply regularly during the infection... not usually very effective.
Try this... place a small palmful of common liquid dish soap in a watering cann and fill with water. Mix the soap and water thoroughly and sprinkle on the leaves of your plants enough to wet them well. The powdery mildew doesn't like water and the soap helps the water stay on the leaves.
Additionally, water the plants regularly... maybe everyday up to atleast an inch a week. Try not to water them during the heat of the day... just before sundown is a good time and it's better if you don't use a lawn sprinkler but water the base of each plant.
Here in the western U.S. where our rainfall is sparse, I like to put about an inch or 2 of peat moss around the base of each plant out about 8 inches or so to keep the roots wet and cool...