This confirmation from the Timeslive website:
The English Electric Lightning aircraft exploded after crashing near the Overberg Air Force Base in Bredasdorp. The aircraft was operated by Thunder City in Cape Town, which offers thrill seekers trips in ex military jets.
Thunder City CEO Mike Beachy Head said the the pilot reported having hydraulic failure and was preparing to eject shortly before crashing.
One spectator who didn't want to be named said he watched as the aircraft spiraled towards the ground then disappear in the bushes. "A second or two later I saw a big black smoke mushroom," said the man.
Anzelle Smit, spokesman for Metro EMS in the Western Cape said after almost two hours of searching the pilot's body was found. "He was found outside of the plane not too far from the air force base," said Smit.