There is a lot you can do before bringing in the builder, assuming you are able-bodied and have a ladder for getting into the attic - but don't inspect the chimney or roof from in high unless you know what you are doing on high places and are properly tethered.
It could be any number of problems.
If its a brick chimney you should check if its got a continuous tray through it.
If not, and the brickwork and mortar is old, water can find a way down through the chimney and into a habitable space.
If its a rendered blockwork chimney, again check for the full tray - same reason.
Then check for cracks in the render anywhere - once the weathering render is broken, driving rain can force the water in.
However none of the above will usually result in damp on the ceiling unless its right beside the chimney.
On the contrary, if its the chimney the first signs will normally be on a wall near or at where the flue goes up.
Ceiling damp can point to a number of other causes.
Check and see if you have a cracked or broken slate or tile, of if the ridge mortar, hip mortar or valley flashing has become dislodged.
Check and see if you have insulation above the area in question; -
- if there is, see if its been wet by a leak- this will create a cold bridge.
- if there isn't, this will be a cold bridge
Cold bridges are well known for creating surfaces onto which water vapour rising in warm air will condense.
This can lead to a damp [in some cases wet!] surface on which damp mould may grow.
Finally, do the obvious and check to see if you've a burst pipe in the attic!
Pipes in uninsulated spaces should be lagged or else routed down below any quilted insulation to prevent frost action.
While you're up there check the water tank is covered with an insulated cover and that any attic insulation is carried up the sides of the tank, but not under the tank.
This allows warm air to rise and keep the tank warm and prevent frost action.
Any other tanks [header tank] or any pipes or fittings rising to or from the top of the tank, i.e. supply pipe or overflow pipes should also be lagged.
Hope this helps