This is exactly why the Party Wall Agreement has been formed.
In the past neighbouring homes had to live with the fact that some damage can occur to their homes during the time when neghbours made changes to their own homes.
This usually was sorted out mutually between neighbours and most of the time a compromise was made.
In some instances however the party that was responsible for the damage would end up denying it had anything to do with their works and court battles would result.
The Party Wall Agreement is now there to protect the neaghbours from this blame shifting and binds that the people doing the works to their home must repair any damage incurred to neighbours home.
In your case the builder has agreed to put things right and it would be great if he does.
Please remember that if he does not want to repair the neighbours house for free he does not have to unless he had agreed to this in a contract at the start of the project.
