A few suggestions for what I'd be doing if this was on my patch and I was trying to prevent demolition.
Contact HE and try and dig deeper on why they haven't listed - if they think there are better examples of late 20th century non-coal headstocks and engine houses, ask them which ones and what makes them of greater importance. I'd also ask if they've consulted their national advisor on minerals issues (Jon Humble) for his opinion on the importance of the standing structures at Grove Rake. Consider what other remains are left in the North Pennines from post-WW2 fluorspar mining and how Grove Rake compares with those other sites, also what remains there are in other parts of the country from that period, then use this to make the case for the importance of Grove Rake in both a regional and a national context.
Also, has anyone alerted Peter Claughton (NAMHO conservation officer) to the threat?
Follow the horses, Johnny my laddie, follow the horses canny lad-oh!