Yes, sciarid fly also known as fungus gnats.

The grubs are about half a cm long, sort of translucent white. Although they eat mainly rotting vegetation, they seem to like soft fleshy roots (eg those of bulbs and cacti), and in abundance can kill the plant. The flies you see will have just 'hatched out' from the grub, so worth squashing as many of them as you can before they go off and breed in another pot. They're fairly easy to squash as they tend to crawl round and round the pot, rather than flying around.

They like damp high humus conditions, which is why you're getting them in damp peat free compost. So, what you can do is:

Kill off any adults by squashing or pyrethrum (but beware beneficial insects)
Consider repotting choice and vulnerable plants in fresh compost.
Cover pots with a layer of dry sand so the soil surface is not attractive to females.
Go over to using soil based composts for a season until you have the plague under control.
Enclose pots of seeds in plastic bags as a physical barrier against the flies
Keep your compost away from the plants, and with the top firmly closed, so that the compost doesn't become infected with them.

By chance, I've found that Nicotiana sylvestris is a useful control in the growing season - the flies are attracted to and get stuck on the sticky leaves and stems, so I grow a few amongst my other plants (Unfortunately whitefly are also attracted to the Nicotiana, and they are strong enough to be able to fly off again))