The Air Training Corps as such did not exist until Feb 1941. Its predecessor organisation was the Air Defence Cadet Corps (ADCC). so you may have more luck searching on that. If records were retained, I would expect them to be at TNA. However a quick search doesn't reveal any records of units, just the higher level policy files. A further quick search of the Royal Berkshire Archives failed to turn up anything, but it might be worth giving them a call anyway.
I suspect that
HQ RAF Air Cadets at RAF Cranwell will be unlikely to be much help, but possibly worth a try.
I assume you've already contacted the present day Air Cadets Squadron: 153 (Slough) Sqdn, The Cadet Centre, 307 Uxbridge Road, Slough, Berks, SL2 5NZ