I would definitely contact the Environmental Health Department at the council. Damp is a serious housing issue and it is the duty of your landlord or the letting agent to fix it. Sometimes however the tenant can be the cause, if you are using the shower without opening the window or using the extractor fan properly. However, this usually only causes slight condensation and not the severe damp you are reporting. Please get in touch with us. It sounds as though there are serious problems with the property and extra 3rd party evidence you have from an inspection from your council's environmental health inspector would strengthen your position if you decide to take further action against the landlord or letting agent.
In terms of your brother's room, if he is not damaging the property the bedroom is his private space and it is pretty poor form for a letting manager to enter his private space. If he hasn't damaged the property and any mess can be cleaned easily then there is no problem.
The main issue is maintenance and the damp which should be resolved urgently.