Condensation, damp and mould in UK houses is most often caused by people draping wet washing around the home and over radiators. If you think that might have been happening, open the windows and the damp air will be replaced by fresh cool, dry air which will absorb moisture from the walls instead of adding to it.
If the house is newly-built, then the walls will have been damp from the water in the mortar and the plaster mix, and possibly also from rainfall before the roof was on. Again, open the windows, and it will dry out, though it may take some months.
Damp caused by wet brickwork can usually be identified because there will be visible brick- or block-shaped patches showing on the plaster.
Emulsion paint itself is made of a lot of water, and needs open windows and plenty of ventilation to dry out fast. But damp from emulsion paint is usually noticable by causing condensation on the windows on the first day or so. If the plaster on a wall has been highly polished to a glassy finish, the paint wil not be absorbed, and these patches (often dark-looking) will be slow to dry and quick to peel.
If the plaster is coming off the ceiling when rollered, it was probably badly applied - for example if new skim was put on a painted surface, or if it has been patched up by an amateur. But have a look in the loft. Lofts are where a lot of condensation occurs, because water vapour is lighter than air, so it rises through the house until something stops it, or it reaches a cold surface to condense on. There is also a chance of a water leak, either from plumbing in the loft (this usually shows as brown marks on the ceiling) or a defect in the felt or tiles.