Thanks all for your feedback.
@bassanclan Not the main wall but sloping walls which are almost 3 feet thicker and 6 feet high and are entirely in my property. They need to be trimmed.
@Temp Good point, I will check with the builder for the site insurance. @kandgmitchell Yes, the new walls would entirely be in my property so there would be two separate terraces. @TommoUK Good point, I will check with the council if it was bomb gap. That's exactly the PW surveyor is doing at the moment.