Sounds like fungus gnats. The adults don't damage the plants but the larvae will damage the roots and leaves. You can reduce the numbers by controlling the amount of soil moisture but also (more effectively) by adding Bacillus thuringiensis to your soil before you sow. You can buy formulations of that contain Bt in gardening centres here in N America (not sure about Europe).
We use Schultz-Instant Insect Spray. It kills the fungus gnats pretty well. IMPORTANT: you have to dilute it about 1:5 or it will kill the Arabidopsis plants. Definitely test it on plants you don't care about first.
From the manufacturer: Schultz-Instant® Insect Spray is made from botanical pyrethrins for the control of insects in the home and garden. Kills aphids, whiteflies, mealy bugs, red spiders, spider mites and other damaging pests.
It could also be shore flies. You can help keep the insect population under control by letting your soil dry out a bit between watering. That way you won't have to use chemicals so often.
Flies that you see come from soil containing larvae you should use preventive. biological treatments at the firm Biobest example. They offer organic solution as Steinernema-System that fights against flies compost. This product is based on a selected portion of a parasitic nematode Steinernema feltiae insects, actively seeking larvae of fungus gnats in the substrate, and then destroy strain. You can also use parallel VectoBac12AS which is an aqueous suspension of Bacillus thuringiensis
for the fight against the larvae of mosquitoes and blackflies. good treatments !
Freezing your soil for 48hrs and then defrosting prior to sowing should also be effective. I've been running an insect-free growth room for 4 years now doing this, but it is also within a containment building so insects coming in from outside isn't an issue, which it might be for you.