Old emulsion comming off when repainted!

I tried painting my on-suite bath room with emulsion which was fine until I reached the area around the sink, the old paint came strait off the wall on to the roller then back on to the wall so it looks a mess I assume it's because there has been water splashed on it over the years.

How do I fix this?

PS, the reason I'm using emulsion is so it would match the bedroom, I have polyvine varnish to finish the new pain job, the old paint is emulsion and I washed it with sugar soap before attempting the new job.

I think jimmy, that the original bathroom paint did not take very well in particular to the surface area around the sink.
As you say it is an en-suite bathroom, would it be a new addition on an old house or even a new build? Is it possible that someone had used a standard vinyl paint straight onto the new plaster without using a thinned non-vinyl paint. If this has happened, it will sometimes come off when using a roller.

You may get away with allowing it to fully dry again, which it will have by now, then lightly sand over the area to key and smooth it, then repainting using a good 3" wide soft filament brush but also try and avoid going over it too heavy handed, leave to dry overnight then apply a second coat. Wait at least a day then apply the polyvine varnish but use a small 4" roller with either a fine or medium soft pile. Again, apply but don't over roll the area as when it is wetted it can start to soften the paint again and it will spoil the work.

Worth a try.

After a second look it looks as if the wall has been damaged/repaired so I sanded it right down and touched up the area with filler then gently painted using a brush as suggested managed to get the first coat on so looking good.

Sometimes using a soft brush can allow paint to be applied quite quickly without disturbing any already dry paint underneath. It's worked for me in the past when I have suspected a patch of paint has not been quite as stable as it should be while I am adding a paint coat.

Good luck with the rest of the job.