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You can tell the neighbour that they are clearly liable to you for the damages done by their contractors and they are required by law to put you in the position you would have been in had this not happened.
You can tell them that you will allow them to get the contractors to do the work or hire someone else. Then say that if you have to hire someone you will be looking to them for full compensation and will sue if necessary.
You can say the same thing to the contractors and if you have to sue you would sue the neighbour and the contractors.
You would sue in Small Claims Court and would self-represent and if it gets that far and you find you need some help as you go through the process you can always post on this site again and I can assist you further.