john west wrote:

Talking to another neighbour she says that she thinks he needs
permission from us to do this work. But what if he just goes ahead with
it anyway?

You can't stop him doing the work, but he has to go about it the correct way

https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/523010/Party_Wall_etc__Act_1996_-_Explanatory_Booklet.pdf