HuwG - Unfortunately I found only one unit connected with the battle of Minden:
Minden Boys, The: The Lancashire Fusiliers. Through the Ist Battalion as the 20th Foot ... (Fraser, Edward: Soldier and sailor words and phrases : including slang of the trenches and the Air Force ; ... / comp. by Edward Fraser and John Gibbons. - London : George Routledge & Sons, 1925. - pg. 191-192). The "unsurpassable six" British infantry regiments are mentioned, but not definitely named except the L. F.
ozmacca - Fine story about your BSM; the NCOs seem only to be able to note single faults, but not uniformly performed ones because no one is sticking out. We did it, too. After a longer salute drill done squadwise the Seargent Major did the evaluation, the platoon passing in a single file and everyone doing a very smart salute (it's difficult in the German way, especially forming the straight line with forearm and side of the hand). Normally he should have gone ekstatic, but he didn't. There must have been something wrong, but he couldn't name it. After leaving boot camp we told him: the entire platoon had performed the salute with the LEFT hand. Draftees' revenge.

Wilfried