Strange fast growing mushroom like entity
This is dry rot. It could be one of several species, including Serpula lacrymans, Meruliporia incrassata and Fibroporia vaillantii. It is a fungus that feeds on and decomposes wood. Despite the name, some moisture is required for growth, so 
it makes sense that your wall suffered from damp. The fruiting body will darken at the center as the spores appear.

Example images of dry rot fruiting bodies:



Photo by Seabrooke Leckie



Photo by Dave Brown