Making Sense of the Party Wall etc. Act 1996
If you intend to build up to the boundary you must serve notice on your neighbour giving them the opportunity to appoint a surveyor http://www.simplifydiy.com/building-works/party-wall
Making structural changes to your property
If in doubt its always best to consider using a qualified designer architect or surveyor http://www.simplifydiy.com/planning-permission
Identifying And Dealing With Subsidence & Heave
Seek professional advice from a chartered surveyor as to whether the trees should be removed or simply cut back to a size that will reduce its water consumption http://www.simplifydiy.com/walls-and-ceilings/subsidence
Planning Permission & Building Regulations
You should give notice in writing to the adjoining owners at least two months before the work is due to commence and they can request that you pay for an independent surveyor to review the proposed work and make any amendments necessary to protect the structural integrity of their property http://www.simplifydiy.com/building-works/extensions/regulations-and-permission