It depends on whether the ceiling is plaster board or cement sheet lined. Unfortunately, mould is like a fungi. It takes a while to grow and ultimately becomes ingrained into the sub strata, which in most cases in a house is the plaster board.
Plaster board or gyp rock as it is commonly known, is basically made up of plaster and paper. The plaster is somewhat similar to chalk and therefore porous. So, unless protected in a wet and often steamy area such as bathrooms, it will ultimately absorb the moisture allowing the mould to grow.
Depending on how bad the mould is, will determine how you treat it. Firstly, I would try to dry the ceiling out as much as possible with a heat blower of some sort, (difficult I know, but the ceiling fan will help once installed) before doing anything else. I would then lightly scrape off any loose paint and mould, bearing in mind you don’t want to scrape off the paper of the plaster board. I would then give it a light wash down with sugar soap and then perhaps as VSYoot suggested, a mild solution of vinegar.
Once it has completely dried, I would paint it with a plaster board sealant before applying your top coat of acrylic paint.
Cement sheet (often asbestos in old houses) is a different matter, and something I would get the professionals in to do.
In the past, I have done the easier thing when the mould has been so bad. And that is to take the whole ceiling down and replace it. But I’m sure you won’t want to do that