As well as the excellent info provided above, a condensed history of 3 CAACU at Exeter appears in 'Devon Aerodromes in old photographs' by Keith A Saunders, first published in 1994. which also includes pictures of the unit's Balliol, Beaufighter, Hunter, Mosquito, Spitfire and Vampire aircraft, A good reminder of those far off days.
On a personal note, in the 1960's I had the good fortune in my teenage years to be stationed at HQ 25 Group, RAF White Waltham, the Flying Training Command Group responsible for a half a dozen FTC stations plus 18 University Air Squadrons and No 3 CAACU. So many nice day-outs for our staff officers, especially during the pre-AOC's season.
From memory, our sister Group, No 23 in the north of England (Dishforth?), may have had 5 CAACU at Woodvale on their books. Regards.