Thanks for the replies!
I am thinking now that it may be water running down the inside of the door. When the car was being restored and had new doors I cannot recall any poly sheeting being put inside. Do either of you happen to have a photo of the inside of the door showing the poly sheet? if so that would be extremely useful!
I think I may also do as mishmosh suggests and fix a poly sheet inside the door to protect the door card. I will also check and possibly renew the seals between the door and the glass.
Thanks again
Paul