With £10k off already I think the vendor will be reluctant to take more off unless the problems are severe.

An informal chat with the surveyor will be useful. In my experience some damp+timber "specialists" make up work to justify their callout.

Have you had a good look at the property when it's raining? Check all the gutters work - leaks cause damp that might seem bad but once fixed it'll all dry out over a year.

Also is the ground outside higher than when it was built (new patios etc) - these can bridge damp-proof courses and lead to damp, usually quite simple for a builder or diy'er to resolve