leaking extractor fan and damp problems in the bathroom

This is quite a common fault with ductwork to the fan not being insulated and the hot air from the bathroom directly extracted thru the duct to cold air within the loft space causing the air to condensate which in turn will make the fan faulty as water in the duct will run back in the room and corrode the fan mechanism. To remediate wrap insulation around the duct in loft space to tile vent or put a condensation box on the duct as it comes out of the ceiling into the loft space. If you still have a problem you also may need to adjust the overrun timer on the fan so it runs 15mins over when you turn the light off to get rid of excess moisture in the room after shower/bath.