Thanks everyone for the advice,
I got a floor standing fan in a store called Argos we have in the UK... except we got it home and found that we had two of one of the parts and another was missing (it needed self assembly)
Hubby took it back and got a replacement and I've put it the far side of the greenhouse from the plants, pointing up rather than direct at them. I can see the leaves waving so I know they are getting a gentle breeze.
I also left the door open last night and all day today and they get a breeze (sometimes quite a strong breeze as the greenhouse is in a windy spot) through that.
With both the fan and the open door and I see that the moss is less soggy than it was. The Catt roots still look really bright green though and I would like to have seen some signs of drying on though.
I've turned it off now as it's getting dark and I don't want them getting too cold a breeze but I'm leaving the door open overnight again.
Time will tell