Answers: Very much doubt it because that would be wear and tear, but the best answer is t read your policy and homily to the insurers
I doubt it. I would think the with the sole purpose rising damp covered would be flooding (well and truly rising damp). There are two things that you vanished out that are critical to a response:
1) What is causing the increase surrounded by humidity?
2) What actual, physical damage to the home have it caused?
The short answer is no. When you look into your policy you will own (almost certainly) two levels of cover; Standard cover and inadvertent damage.
Standard is fire, flood, impact, burst pipes, raid, storm, that sort of thing. If your loss does not fit into one of the category ("Perils") then you hold no claim. Accidental damage ("AD") extends standard to include AD. The typical wording is " ... sudden bewildering, external damage excluding power-driven wear & tear and leisurely operating cause ... " Rising soggy may be specifically excluded as most definately dry rot will be or whether it will be classesd as a "gradually operating cause".
I know this doesn't lend a hand but it explains in detail exactl why you will not pass.
xxFJ