Hello, Sophie!
They sound like fungus gnats. Sometimes they are a symptom of overwatering, but, once established, they are likely to persist no matter what is done with soil changes or watering control. I've always favored products containing beneficial nematodes or Bacillus thuringiensis israelensis, since they are non toxic to kids or pets. Also pour chlorine bleach or rubbing alcohol down the drains, since they will also colonize the upper sewage system.

yes they do sound like fungus gnats. letting the pots dry out almost to the point of the plant wilting will also help kill the small larvae in the compost. You could put the sticky traps next to your pots to try and trap the adults. Both of these have worked for me. You can also get some insecticides that will target them. Follow the instructions on the bottle if you go down that route.

This is the advice from the RHS

https://www.rhs.org.uk/advice/profile?pid=804