I believe it must have come from Height, Health and History by Roderick Floud, but I can't find a digital copy of that book to link, despite it being 30 years old. The closest thing I could find is another work citing Floud, and only with regard to the difference in height at the beginning of the 19th century. It gives "nearly 6 inches taller", but note that it's comparing 14-year-olds in 1800, when nutrition for the lower classes was on the upswing.

> Floud et al. also showed that men who grew up in urban areas were shorter than men who grew up in rural areas, and that there were significant differences in the heights of men and boys from different socioeconomic backgrounds. At the beginning of the nineteenth century, 14-year-old boys attending the Royal Military Academy at Sandhurst were nearly six inches taller than their counterparts in the Marine Society

https://core.ac.uk/download/pdf/6876106.pdf (bottom of page 101).