Hi Jon and welcome to GoY could you post your pix into the question please so we can look at more easily.

check my chillies out - what type are you trying to grow?

The obvious answer would be an infestation of some sort.
One question springs to mind though - where in the house are you growing them?

Pix posted to my picture page.

Sorry not sure of the make/model (ha!) - but all the edible ones seem to get the same problem.

I'm growing them either on the sunnry (SE facing) window or on the mantle piece - which is in a large S facing room (glass on three sides).

I think you are experincing an infestation of spider-mite. I have a Chilli I grew from seed in 2005 and it lives in my bathroom woindow which is southfacing and light. It sounds to me like you have it in the right position so I wouldn't worry about that. My chilli has had spider mites a few times so they can recover. In the first instance, I would pick off the worst affected leaves to try to contain the mites. When you see the 'fluffy' bits just wipe it off with your finger. Then you can give the plant a solution of water with a tiny bit of washing-up liquid in. Use a mister and make sure all of the plant gets misted, under the leaves especially. Leave it for a wekk or two, and keep picking off the worst leaves, even trim the branches if they are especially badly affected. If it continues to suffer, repet the soapy shower or get an approprite chemical pest colntrol from your garden centre. The main thing is, a chilli will usually recover from spider mite although it looks dramatic. Mine has survived for 4 years. Hope that helps. :)

oh and spider mites are so small you can't see them, so don't dismiss them just because they aren't visible, chillies are prone to spider mite.