I've just stripped lining paper in a largish bedroom, 4m x 4m x 2.9m;
unfortunately the plaster is covered in patchy distemper.

From online research it seems that there are two types: water-based
distemper and oil-based. Since mine rubs off with a damp kitchen
scrubbing sponge I'd guess I have the water-based distemper.

I know I need to seal the surface using one of (1) clear stabilising
solution, (2) primer sealer, or (3) diluted PVA prior to applying
emulsion paint.

Can any of these sealers make the surface smooth enough that
subsequent coats of paint won't show the underlying patchiness, or
must I wash all of the distemper off first? It took me about 15
minutes to wash 1 square metre, and I'm not sure I want to spend 12
hours scrubbing walls!

Dave