Clearly this is a serious structural issue and your home will require extensive works to repair.
You made a claim under your NHBC warranty in 2020, which is in year 9 of your 10-year structural warranty.
I can see no point whatsoever in digging holes and monitoring the movement of the structure of =your home.
From just the one photo you posted it is clear to me that you have either heave, or more likely subsidence.
The cause could be due to the proximity of a tree, poor ground conditions, leaking water mains or drainage pipes (perhaps not even from your property)
So the NHBC should excavate to discover what the cause is and then a structural engineer can design what needs to be done, usually underpinning the failed foundations, after which the brickwork can be repaired.
You should be aware that your home now had a "history of subsidence" and as such you will have to inform any potential buyer and your insurance company who will no doubt drastically increase the subsidence excess and perhaps the cost of buildings premium too!
Which builder built this house?