It is definately MDF (I've used chipboard etc. before), I'll try to explain a bit better...
If you run your hand over it quickly, it feels smooth as normal. The 'bits' are only apparent when very slowly running your hand over it (they just feel like very slight bumps). Even after priming, I could still see the MDF (thru the thin primer), although it didn't look bad. Having applied the top-coat, the 'bump's are clearly visible. Wierd.
It is as if the powder that it is made up of had some bigger bits mixed in with it every so often. I don't have a close up photo atm, and from a distance it is impossible to see.
I don't know where I would get veneer, so I might try sanding it. I am not sure if filling will work as there are relatively few high spots (bumps) in comparison with the 'normal' surface. It doesn't have a pitted surface like chipboard.
Thanks guys, I'll see how it goes...