The NHBC does indeed stand for National House Building Council. They are the same as Premier Guarantee and offer warranties on new homes and nothing else. They will only act when the home has an NHBC warranty.
The Premier Guarantee Warranty is a structural warranty.
https://www.premierguarantee.com/our-services/structural-warranties/new-homes-warranty/They may be trying to fob you off by implying that it doesn't cover subsidence caused by non-construction on issues (storms, tree roots etc) but if standards have not been followed, a claim is justified.
It's a long process, but you could make a claim using the Financial Ombudsman Services as The Premier Guarantee is an insurance product. Be sure to have independent valuations of your increase in insurance premiums and reduction is market valuation due tot he underpinning history.
Again I suggest that Linden buy the house from you as the easiest option and you walk away.
The alternative is many years of battling both Linden and Premier.
see Tweet below! Worth your while you contacting Yvette.