Hello I am a solicitor with over 15 years experience. I will try to help you with this.
How many of your mother in law's walls are damaged? It certainly sounds like your neighbour is likely to be responsible for compensation and depending how bad the damage is he can be ordered to carry out repairs too. Your mother in law needs to get some evidence, perhaps by instructing a surveyor to carry out an investigation into the problem. He will be able to advise on likely source even if he can't get access to the neighbour's house.
Depending how serious the problem is then she might want to see a solicitor and get them to instruct a surveyor for her with an eye to potential litigation. A solicitor can be found via this link. http://solicitors.lawsociety.org.uk/
Legally there may well be an action in negligence or nuisance against the neighbour.