White patches on the leaves and stems of courgette plants are caused by a fungus called powdery mildew. Members of the cucurbit family (courgettes, cucumbers, pumpkins, squash, melons etc) are especially susceptible, and if left untreated, the plant will weaken, and you may lose your crop.
Powdery mildew is associated with water stress, so it is important to water your plants regularly and not to let them dry out.
If you do notice powdery mildew on your edible crops, then remove infected leaves and dispose of them in your green bin or bonfire. Threre are no chemical treatments for edible crops.