Extractor Fan Duct in Roof Leaking

We have started to get water dripping through our en-suite Extractor Fan, but only when it’s raining. The duct goes directly into the loft, and up to the roof where it goes into a plastic vent. The leak seems to be coming from the lip on the vent overflowing rather than a leak in the roof itself. Is this fixable at a DIY level, or if not who (in terms of tradesman) would come and repair this? Plumber / Roofer? Thanks