I have recently been shooting some footage in quite dark settings, but with one single light source which was shown on screen. I notice each scene has 2 light spots, almost like fire flys moving around the light. One moves horizontally and one vertcally.
Does anyone know what causes these and what can be done to prevent it happening?

Could be lens flare caused by reflections in and between the elements of your lens. To avoid it, try to keep the lamp out of shot and use a lens hood or barn doors on the camera to avoid the light from the lamp falling directly on the front element of the lens. Polarising filters can help but sometimes make it worse by adding another surface to reflect.

Belated welcome to dvinfo by the way. I am keeping a note of the Brits posting here (found 334 so far!)

Thanks. Yes, i think they must be internal relections of some sort. I am using a Matte box and flag. The light source in question is actually an "electric" candle, which has to be in shot to light the subject.
I am not sure if I have the lens on AF or MF during these shots. It could be the AF hunting i guess. I will set the shot up again and try it on MF.