Go to B&Q and buy some Polycell white fine surface filler. Get a plastic surface filling tool - one of those flat applicators with one chamfered edge.
Moisten the bare plaster areas, and apply the filler thinly over the blemishes. leaving as little excess on the surface as possible - don't worry about a perfect finish at this point.
When the filler is thoroughly dry and hard, use a sanding block with fine-grade green sandpaper and remove the filler until just the damaged areas are filled. They will not be perfect, but now you go over them again with filler (after you have wiped the area with a damp cloth to remove all traces of sanding dust.
When that application has dried do the sanding process again, and this time go gently and carefully.
With patience, you'll end up with a perfect surface, onto which you can apply two coats of paint (after you've wiped of all sanding dust again).
Good luck, and ignore anyone who tells you that you should use a filler knife for this job.