Rhodesian Army base that had been an airfield
That narrows it down to two places; Kumalo and Heany. Kumalo was a headquarters unit with a couple of comms aircraft; later to become the Territorial Army HQ. RAF Heany became Llewellan Barracks, again a TA training unit.
I was at Heany as a service brat in 1950-53 and at Kumalo and Llewellan as a Terrier in 1958-59. Did not hear anything about Spitfires being tucked away.