It’ll only be National Grid if you live in their gas network area, different areas of the country are owned/operated by different companies, though usually this type of work will be done by outside contractors, it all depends.
If you are worried, call the network and explain, you will usually be able to ask for someone to visit you and explain. Try to speak to the project manager or similar.
As above, more than likely they will be able to do it without digging up, but if you’re not in and they have an issue doing it, they won’t wait to speak to you before they get the jackhammers out. You need to make it clear to them that this would not be at all acceptable. The problem is, that they won’t know exactly what they’re dealing with until they start doing the work. But the vast majority of the gas networks are doing everything possible to avoid complaints, so don’t be shy about getting in touch with them.
Again, message or email me if you want more info.