There have been interesting studies of the Falklands, which suggest that the sprinter physique favoured by some is in fact poorly suited to prolonged combat. Endurance (measured in days and weeks) is preferable to a no-fat, lean runner's physique.
The study had a pretty clear outcome: Special Forces, Parachute Regiment and Commando Brigade personnel were able to hack it, largely because of their ruthless physical selection during recruit training and regular ongoing battle fitness oriented training at the units afterwards.
The others? Not so much.
There were many noises made about trying to upgrade the rest of the Army's fitness to close in on that of the Paras and Marines but, as with most lessons learned in war, it was forgotten in the rush to peacetime. No one wanted to admit that over 70% of the infantry could not do a big march, then fight.
The quote you may be thinking of could be from LCpl Vince Bramley's book, Excursion to Hell, referred to in this article here (p.18 onwards) http://www.seanmmaloney.com/wp-content/uploads/2016/02/D12-9-2-2E.pdf
3 PARA marched 75 miles in three days across mountainous terrain, each carrying loads upwards of 100lbs, then fought the Battle of Mt Longdon at the end of the hike (the Royal Marines performed similar 'feats of feet'). In the book he mentions that everyone visibly lost weight and those that had more to lose tended to be able to keep going longer. None of these 'heavier' guys would be classed as fat though, that's for sure. Your average PARA is about 5ft 7in tall and usually well under 190lbs... the 'Poison Dwarf Brigade', indeed.
To my knowledge the British have never had any biometric BMI-like BS as part of their fitness programs. It all tends to be performance related, you know, like real war.