The March 1963 issue of Four Wheeler Magazine included an article by Brian L. Pinn about the Anglo-African Trans-World Safari, the pics and text of which can be found at The FC Connection.
It turns out there’s a bit more information out there, though not as much as I’d hoped to find, especially given that the group of travelers that made up the trip had access to cameras and film and also given that in January 1963 American Television script-writer John Hicken was supposed to join the group to film the around-the-world adventure.
Without that storehouse of info, or a book, or a movie, we only have the following scraps to better understand the adventure.
South African Derek Linton came up with the idea to travel the world in 1958. At some point, in order to gather equipment, Derek travelled to the United States in 1959. He was photographed at a Ham Radio station in Burlington, Kentucky, a visit later reported in the January issue of Short Wave Magazine:
This map shows the proposed route:
On September 19, 1961, a photo of Derek Linton and Gerald Cubitt (unsure who he is) was taken by Henry Bush. It’s part of the Henry Bush collection at Shutter Stock:
In the July 27, 1962, issue of the Warren County Observer, a syndicated article appeared by John P. Callahan that shared the news of how the idea for the trip originated and the progress the travelers had made:
Finally, on January 05, 1963, the Evening Standard (London, England) reported that John Hicken was going to join the crew:
In March 1963, the Four Wheeler article appeared.
There is also a mention in a 1963 issue of Business Week about the travelers, but I’ve been unable to determine which issue.
After that, I have been unable to learn more about the journey.