Why are my seedlings dying

They like damp compost to lay eggs in. The larvae are like tiny, translucid worms that glide through the top couple of inches of compost. Perhaps the flies are searching for an alternative maternity ward that's just been watered

 

They are less of a problem if you get into the habit of watering from the bottom.

 

Errrggg!

Job for today.......!
Replace top two inches of compost and get a bottom watering system worked out and set up!!

Thank you @noisette47 and @pete for your replies. Just wondering.... last summer I took all the plants out into the garden and gave them a good soaking (in the dog bath), would them being taken outside have helped or hindered them? It’s pretty cold out there today but shall I take them outside for a while, would the cold help kill of the flies or just hurt the plants do you think? We are in north Essex.

 

I wouldn't put house plants out on a day like today.
Soaking them is good for once in a while but it does make the compost very wet which the blighters will like.

 

Just stock up with matches, Tinks It really does work!