If the summer is poor, courgette plants may respond with poor pollination. Courgette plants produce male and female flowers. A female courgette flower has a bump, or swelling at the base, which is the immature embryo fruit. This is how you identify it as a female flower compared with the males stems, which are straight with no bump. In the image, the male stems are marked and straight, the females have a swelling, which becomes the courgette.
If the summer is poor you can help pollination. Pick a male flower, remove outside leaves and then brush the anther (middle bit of male flower) over the inside of the female flower (stigma) and it should pollinate. One male flower can pollinate several females. This makes it sound as if growing courgettes is difficult; it's not, and normally the problem is the glut of courgettes, which is why most gardeners only grow a couple of plants. Because courgettes like it warm, they usually pick up later in the summer, so if there are no fruits early in the summer there is no necessity to hand pollinate. You can just wait for the weather to improve.
If you notice the fruits dropping off and rotting before coming to maturity, this is caused by a lack of pollination.
Good varieties of Courgette to grow are 'El Greco' usually prolific, mid-green fruits and good disease resistance. 'Supremo' is compact, so good for smaller gardens, or containers. If you are looking for colour 'Parador' is a bright yellow variety and 'Defender' is a F1 green variety. These recommended varieties have the RHS award of garden merit in the 2021 trial.