I grew chilli plants a couple of years ago and they did wonderfully well. To be honest they did far better than I expected given we started to gut the house and all plants were put outside and left to fend for themselves.
This year I've been a little more precious about it all, they were germinated in a propagator and repotted once they got to a suitable size. Since then they have resided on the conservatory windowsill.
My problem is they haven't grown since then... at all! I took one out and couldn't see much of a root system so I think the problem is they shared a tray with some repotted tomatoes for a while and have suffered from over-watering.
Can plants recover from this? Or should I just get rid of them? They haven't died, they are just not growing.

I'd be tempted to try and revive them because they're quite slow to germinate if you have to start again.
I'd put them in the sunniest warmest place you can find and let the compost dry out a little. It they've been subjected to low temperatures they're quite likely to be retarded.
A friend and I are growing chillies from the same seed sown on the same day. His have been subjected to much lower temperatures than mine, and are less than half the size of mine. If they were repotted into fresh compost that still has plenty of nutrients in it, I'd just be inclined to be patient. You'll probably find that under different more favourable weather conditions they'll suddenly start to take off.

Chillis love the warmth, and I make sure mine are never too wet, that usually makes them unhappy

Thanks, I've kept them in the conservatory and haven't watered them much so they've dried out. A couple of them seem to have put out a couple of new leaves so fingers crossed.