Elevations of climbable mountains weren't then and aren't now determined by triangulation to known landmarks; it would have been done by "spirit levelling," which is, more or less, a local measuring of one's vertical change along a path from an already established elevation which, in turn, is ultimately tied to sea level. Elevations determined by sightings to remote landmarks, as in this film, would be very imprecise because of atmospheric refraction. Indeed, if such a technique could have worked, the hill elevation could already have been determined by measurements from the supposed reference landmarks. A resurvey of a hill that might have turned it into a mountain would have been a differential measurement. The surveyor would only have had to measure the elevation change between a nearby point that he had already passed through on the way to the summit, and the modified summit.
Betty asks Reginald why he isn't at the front and he replies that he was, at Verdun. The Battle of Verdun involved the German and French armies, so it is most unlikely that he was there. It is more reasonable to suppose that he was involved in the Battle of the Somme, both of which were fought during 1916.