If you have an underground ducted feed than comes up against the external wall that is to be worked on, then an NTE ( master socket ) shift isn’t going to help, if the existing duct and external cable is in the way of your building works you need ‘diversionary works’ to relocate the service ( this is something commonplace but normally on a much larger scale , like road widening where existing OR services need to be moved before the excavation starts ), this work isn’t don’t for free.
The whole process, survey, costs, accepting costs and actual work, needs to be done before your building work starts, if you want to ensure you don’t lose service.
As far as who to contact, the duct and external cable is Openreach’s, so they would be my first port of call , not your service provider , BT could arrange moving the socket , but that wouldn’t move the feed to the socket, just the socket itself.
This is for an underground service, if fed from a telegraph pole, it’s a simpler job.
