This isn't the whole story. During WW2 ATC did permit Cadets under 16 to join, but 16-18yr olds were the priority (along with 'deferred service' 18yrs+).
A major clue to the existence of under-16yrs Cadets in 1941 was of course the many ATC School squadrons (in both state and independant schools).
The school leaving age was 14 in 1941, which was increased to 15 in 1944. Cadets that started their ATC career in a school squadron could in principle stay on at that unit until they were called-up, especially if they held rank.
Indications are that Cadets who were edged-out (as opposed to aged-out) from school squadrons, due to the influx of new generations of eligible recruits, would migrate outwards to provide a nucleus for the formation of new squadrons and detached flights.
Another major factor in the whole UK Cadet movement post-WW2 that's remarkably under-documented was the National Service era, right through to the 1960s.
Young men at school or college joined specific arms of Cadet service (ie Sea, Army or Air) so as to ensure that they were streamed to join the particular branch of the armed services that they (and their parents) wanted them to serve in.
This was obviously based strongly upon traditional Army regimental & corps affiliations to different territorial recruitment areas in the country, and a similar situation applied for ex-ATC Cadets automatically becoming RAF National Service Officers & Airmen (the choice of joining a particular branch of the Cadet Forces was obviously influenced a lot by what branch a young man's parents and siblings had served in during the war, and also after 1947, what element of the reserves an individual Cadet's relatives were serving in).