We had this problem the first year we moved into our current home. It's great fun chasing all the flies with the hoover - use the "crevice tool" and suck those suckers up! If you're worried that they may find their way out when you turn it off (which is unlikely) you could take it outside to empty or block the sucker end up with a bit of wadded kitchen roll that you take out next time you want to use it.

Alas, I have no vacuum cleaner. Mightn't the plant disappear up there too!?

An old (as in aged) friend told me to make up a bowl of warm soapy water(soapy, as in washing up liquid), take the plant outdoors and keep flushing the liquid through the soil/compost in the pot until you've used it all up. This apparently kills the flies! I tried it once - and it worked. However, you're not to do it to the plant too often as it does not do it much good. Worth a try.

You don't hoover the flies when they're on the compost Jonathan, you get them when resting on solid surfaces (walls, ceilings, light fittings...) or, even more fun, in mid air. But if you don't have a hoover you won't be able to play. Could you borrow one?

That sounds enough fun to go out and look for an infested plant, Beattie. Do you keep a record of 'catches'? Sorry Jonathon - not much help to you. Make sure you're not overwatering - that always seems to make it worse.
Somebody on another site put 'They seem to be attracted to white, so I leave a sheet of A4 paper on the windowsill, they congregate and I squash them. A sticky trap works too: I had a bottle of almond oil which had leaked, and loads of gnats drowned stuck themselves in it.'

whats wrong with a very light spray of fly killer thats what i use thow i have to be carefull as they seam to like hanging about in my fishtank lid .

Soapy roots. Hmm! I could try on just one and see if it seems adversely afffeted.

Weak tea often will get rid of them, too.

Weak tea!!! I love the idea. I will try giving them a drop of my favorite Earl Gray. I drink nothing else.

My house was infested with the little critters a few months ago and I found that whilst I was away, my husband had forgotten to empty the small bin that we used to collect the peelings/vegetable matter for the outside compost. As soon as it was emptied - no more flies.

Hi folks, I just spent two hours sitting in my doctors waiting room. Had nothing better to do than read all the magazines that were on display. In one of the magazines there was a great little idea for dealing with these naughty flies.
Take 10 cloves of garlic and crush them and then cut into small pieces. Cook these in one litre of water and then let seep for about 24 hours. Use this "water" to spray your plants. The article says it works. Another snippet of wisdom suggests that the main problem is in the fact that the flies seem to propagate in the soil itself. So it was suggested that one cover the top centimetre of so with sand. This apparently acts as barrier to the flies. Good luck with your plants!

Fungus gnats- that's what they are called. Have a look on Amazon. Cures seem to be good but expensive. Sand layer sounds good, bugs that kill them seem good but gonna try tea