I studied drosophila for my Phd Thesis...and did loads of experiments on them - breeding them, radioactively labelling them...and chopping off their heads...but that's another story...
I also have a compost bin and had problems last year...they aren't considered a health hazard though (they don't do spitting and stamping in s**t or eat rotting flesh...like house flies or blue bottles) but...
We used traps of flasks filled with alcohol and banana skins for escapees in the lab (not the RA ones obviously -they just weren't given the opportunity to escape...)...these worked quite well. Also malt or cider vinegar with washing up liquid in it in a jam jar partly covered with cling film or foil will attract them and drown them. Put it near your fruit bowl.
They are most interested in rotten fruit so try and make sure there is nothing a bit overripe in your fruit bowl. (They love banana)
In your grass bin covering the peelings will keep them down ...maybe keep some grass to one side and put a layer over the peelings...the eggs already in the peelings etc will hatch and larvae will crawl up to pupate - so in the short term you will still have flies but if you don't give them the opportunity to lay eggs on anything the population will go down - an old piece of carpet tightly fitting the top will also help...just take it out for emptying. You could try attaching a fly paper to the lid as well..but they never seemed to work in the lab.
If you have a compost bin the carpet and covering works well...this year at the begining of summer I put a thick layer of the compost from the bottom over the top and have been religiously covering all the kitchen waste I put in there with screwed up paper or cut grass - also have been using compostable bags - but to be honest I tend to use them more than once -so some food goes in there bagless...and I haven't had a problem this year...so far...
Also if you store stuff in the kitchen before you bin it make sure what you keep it in has a tightly fitting lid...just one drossie can lay hundreds of eggs in just a few hours...
I would tell your council though ... they should be able to suggest something (like allowing newspaper in there...) after all they want to encourage recycling...