It is probably water lying on the ceiling, or even still finding its way through the floor.
Best idea is to poke a few holes through the plasterboard with a skewer or similar so it can escape, and put a bucket or saucepan under each. A dab of filler will repair this very easily when it is dry.
depending on the age and construction of the building, the occupants with a wet floor should lift carpets and floorboards so that air can circulate and the water dry out.
I suggest you call your insurers in the morning and ask for advice. If there is damp they may lend you air blowers and dehumidifiers, they might want to do more. They would probably make a ckaim against the people upstairs, so the sooner they know, the sooner they can collect evidence.
If the water is coming into the kitchen, try to protect the kitchen cabinets especially. They are usually made of painted or laminated chipboard, and will turn to mush if they get wet. If they are already wet, take out any glass or china if you can, in case the shelves give way.
I see it is a Georgian house. It's likely the ceilings have been replastered since it was built, and there may be an additional layer of plasterboard. Water can lie between this and the original ceiling, I have known one drip for more than a week, until the loss adjuster realised what was happening, and had the builders pull it down.
If it is an original L&P ceiling, parts of it may come down on their own, Another reason to seek assistance from you insurers, they may decide to move vulnerable property and carpets, or provide waterproof protection. In an old house water coming through a ceiling can be very dirty and may cause staining to carpets and furniture.
Sorry.