I'm not so pessimistic. If the problem was ENTIRELY the fact that an emulsion paint had been used over an oil based paint, then not only would there be peeling everywhere in the bathroom, but most likely the painters would have done the same thing in the other rooms and you'd see that peeling everywhere.
The fact that it's only occuring at the most humid places in the most humid rooms of the house suggests to me that the problem lay almost entirely in the fact that an inappropriate paint was used to paint those bathrooms.
I think what you have is a combination of two things:
1. Some paints simply loose their hardness and adhesion in damp conditions. In particular, paints that use a polyvinyl acetate binder are notorious for this. Unfortunately, these will be the less expensive "value priced" paints that are most likely to be used by someone who is either wanting to sell a house or doesn't know enough about paint to know the difference between a cheap paint and an expensive paint.
2. Some other factor that is helping or promoting the loss of adhesion of the top coat from the one below, like the use of an emulsion paint over an oil based paint as Zampa suggests.
(To see if the underlying paint is an oil based paint, clean it with a tissue damp with nail polish remover. If the nail polish remover dissolves the paint rapidly, then it's an emulsion paint. If it has much less of an effect and takes a lot longer, then it's an oil based paint.)
Here in North America (and I expect it's similar in Britain), emulsion paints are made primarily of two different kinds of plastics;
- Polyvinyl acetate (which is what you probably know better as white wood glue), and
- Polymethyl methacrylate (which is what you probably know better as "Perspex")
In both cases, the plastic consists of tiny hard transparent and colorless particles (called resins) that are about 100 to 1000 times smaller in diameter than a human hair, or from 5 to 50 times too small to see with the naked eye. These resins coalesce as the paint dries to form a clear film with the paint pigments suspended inside, much like the raisins in raisin bread.
NOW, there are many different kinds of polyvinyl acetate resins, but paints made from polyvinyl acetate are generally considerably less expensive than paints made from Perspex resins. Also, paints made from polyvinyl acetate share some of the same characteristics as white wood glues which are also made from polyvinyl acetate, notably that such paints have low moisture resistance.
That is, paints made from polyvinyl acetate will lose their hardness and their adhesion under moist or humid conditions, and this is to a large degree why the paint is peeling WHERE it is, high up on the wall (cuz warm MOIST air rises) and over the shower (where water spraying off the top of your head hits the ceiling).
Unfortunately, because paints made from polyvinyl acetate are also less expensive, much of the problems people have with paint stem entirely from the fact that they don't know enough about paint to know which paint to use under different circumstances. As a result, they use an inappropriate paint in a bathroom, which is what we have here.
In your case, someone probably used an inexpensive interior wall paint, not knowing that it's not really suitable for a bathroom. That inexpensive interior wall paint was made from polyvinyl acetate resins and had low moisture resistance, and that's most of the reason why it's peeling WHERE it is.
I agree with Zampa that what you need to do is scrape off the loose paint.
Sand down the underlying green paint with some sandpaper to ensure good adhesion of the next coat of paint.
Then, paint with a paint INTENDED to be used in bathrooms like Zinsser's Permawhite Bathroom Paint which is a tintable emulsion paint that comes in both satin and semi-gloss.
Bathroom paints will be made from a Perspex resin that's particularily moisture resistant (which means it won't soften or loose it's adhesion under moist conditions) and will also contain mildewcides which will keep the paint free of mildew for a very long time.
Covering the PVA paint you have that is sticking well will essentially solve the problem with it because the Perspex paint you put on top of it will keep that PVA paint dry. That is, top coating over a PVA paint with poor moisture resistance will prevent further peeling of the PVA paint by keeping that PVA paint dry.
You can learn more than you want or need to know about paint by spending some spare time at:
http://www.paintquality.com