We've just had some building work done, and we've got a massive tub of plaster primer paint left over. Can we use it in place of normal white emulsion (for ceilings, walls, etc.) or is it restricted to new plaster?

I wouldn't use it as a final/topcoat - it's likely to be powdery and probably wont take wiping down

It's not likely to be powdery or it would be a pretty bad primer. Maybe chalky is a better word, but it should not produce powder on your fingers.

What it won't do is provide any kind of luster (going to look dull) nor will the finish look as homogenous as a good quality top coat paint.

Bad choice for anything other than its intended use in a space that you want to look good. Even for ceilings, a quality ceiling paint makes a big difference to the overall appearance of the room.