I think the LSB schools would have been elementary schools only (the normal school leaving age was only 12 or 13 at that time) and such records as survive, and various anecdotal recollections, suggest that canings at such schools were usually given on the hand, typically 1 or 2 or 3 strokes on each hand. Three on each hand does make six, but I don’t think that’s what is usually meant by the phrase “six of the best”.
I think a more likely means in which this idea was popularised is the public school stories that practically every boy once read in weekly magazines like Magnet, a tradition carried on by the Billy Bunter books and their many imitators and later by Jimmy “Whacko” Edwards on film and tv.