I can hear running water and loud dripping sounds generated by the flat upstairs.

There is no evidance of damp areas or mould on my ceiling and walls, but could they have a leak that needs to be rectified?

Thanks

It doesn't have to be a leak. It may be water dripping into shower drain or toilet drain. If you have plastic drains then that sound if very audible, especially at night. If it is an active leak within your ceiling than you should know about it within a day or so. Back to you. Milo