My name is ***** ***** I will try and help you today.
Ultimately, the property belongs to the owner so you should try and contact them and deal with them directly.
Ask the Managing Agents who owns the property.
If they do not cooperate, you can make a search at the Land Registry on their website at HMGov.LandRegistry.UK for a minimal fee to see who is the owner as long as you have the address and post code of the property.
Then contact the owner and ask them to rectify the problems.
If the problems persist, you can sue them for damages for causing damp but it would be better to obtain a survey first to confirm the source of the problem.
Similarly, with the tree if the owner is unhelpful you can either sue them or cut the tree and demand reimbursement from them.
If you need professional help to do this, call the Law Society on 0207(###) ###-####and they can recommend local firms of solicitors who can help.