Water leaking in ceiling when central heating turned on
You have a leak, obviously.  Water will travel along pipes, wires, framing, etc so it doesn't mecessarily have to be leaking right above where you see the water. It could be a hole in a pipe, bad fitting, etc. 

You're going to need to rip up your ceilings (usually easier than floor since it's just drywall versus a flooring material) to find out where it's coming from. 

Letting it get to the point where the ceiling collapsed wasn't a good idea. Wet material grows mold. After you fix the leak there is a good chance you are going to have to replace a lot of other rotted or moldy material.