I can't see it coming down the cavity wall if the roof is OK, as the roof and tiles should bridge that gap. I would suggest that maybe the wind is blowing the rain under flashing or the join twixt the conservatory and the house. Alternatively have you any water pipes in the roof space that could be causing the problem?
another possibility is a crack on the outside of the building near the lintel which is allowing the ingress of water. Can't give you the name of anyone but good luck anyway.