Lt Col Robert Wiles said he was "very confident" that the vehicles would endure the journey.
"They might be 83-84 years old but we've done loads of preparation on them," he said.
"We can almost rebuild a jeep with the volume of spares we've got."
He said the problem they had faced was a "charging problem with an antiquated charging system that is quite fragile".
"That was rectified within an hour," he added.
The group will be auctioning the passenger spot of the cars for each day of the trip to raise money for veterans' charity, the Light Dragoons Charitable Trust.
Lt Col Robert Wiles called it "a really ambitious and unique tool that's never been done before" and said they were trying to "raise a significant amount which would make a difference".
