First of all I'd tackle the cause. Is there an extractor fan fitted? If not that would help enormously. I assume there's a window; if you can, leave it open as much as possible. Scrape as much paint as you can off. There's no need to clean it with bleach or harsh chemicals. A solution of sugar soap in hot water would do. But the most important thing before you paint is to apply a coat or two of stain blocker. This will prevent the mould/damp showing through. DIY shops will have it, you use an ordinary paintbrush to apply it. It stinks to high heaven, but does the job!
Yep, there is a window, which is always open. There is an extractor but it's a bit rubbish. Basically it's a really tiny bathroom in dire need of redecorating, but I can't afford to do it all. So I'm just going to tackle the ceiling for now. Baby steps
Thanks for the stain-blocker tip. That's great. I didn't even know there was such a thing!