Your ceilings are almost certainly ‘lathe and plaster’. Movement in the structure over the years has caused the cracking, and the bonds between the lathes (strips of bendy wood nailed to the ceiling joists to provide a textured surface) and much of the plaster will now have been lost. This would be a nightmare to patch up. It’s more common to strip all the plaster and lathes down (a really messy job) and afix new plasterboard, which can be skimmed to form a flat ceiling.

Alternatively, you could ‘over-board’, ie fix new plasterboards beneath the existing lathe and plaster by screwing right through to the joists above. But this will put additional weight onto joists that may not be man enough to carry such loads. Also, if the old ceiling is not level, it will be tricky to correct this by over-boarding.

Double-boarding means two layers of plasterboard are used rather than one, giving greater stability and better sound insulation and fire resistance. However, it takes up more headroom, costs more and weighs more. Two layers of standard plasterboard usually provide a half-hour rating for fire resistance. Pink-faced ‘fire-line’ boards achieve the same level of fire resistance with only a single layer.
Answered by Hugo Tugman