The rain has just poured in through the top of the back door! About a pint came in during a massive downpour, soaked two tea towels and most of a kitchen roll which I used to try and block the flow. The only way I could stop it coming down off the roof and through the seal was to open the door and let it fall past the van like a waterfall.
This answers the question about the damp carpet...
The ultimate solution was to turn the van so the cab was lower than the back door, so the water ran over the windscreen.
And as I type, here comes the rain again...
