Read the moneysavingexpert forum then ask for advice there:
Forum
A few on this forum work in this area, maybe give it a bump in the day. I don't know if there is legislation about damp, but I'd doubt it would be relevant unless the house was very bad.
The way I see it you have a few choices.
If you refuse to sign, they can say ok and let to someone else giving you I think 2 months notice if you're on a rolling agreement. They might of course fix the damp! Depends on how much they need to keep you, and if the LL can afford the work.
You could sign and hope they'll fix the damp. Not gonna happen, as your experiences so far show.
You could find another place. Rental market is supposedly very tough for landlords at the moment, so you might get a better deal. Certainly rental prices around here have stalled and then fallen over the last year. If there are lots on the market you can negotiate a good rent.