Stalwart Across The Channel
Investigation of the Times archives has indicated that something like this did actually occur. Specifically, the following was reported on the 24th November 1965:
ATTEMPT TO DRIVE ACROSS CHANNEL
Hohne, Nov 23- A Rhine Army trooper from Bristol who tried to cross the English Channel in an Army five-ton amphibious vehicle was sentenced to eight month’s detention here today. He was found Guilty of being absent without leave and three other charges. He entered the water from Belgium but had to land near Calais, where he was detained. A District Court Martial was told that Trooper Robin Wilfred Painter, 20 of the 11th Hussars, had planned to England after a 400-mile drive from his barracks at Hohne. He then planned to cross the Irish Sea from Liverpool to Ireland where he had planned to ditch the stolen vehicle.
In a statement he was alleged to have made to the military police Painter said he took the vehicle on September 22 and set off to drive to Belgium. At the time he was under open arrest after a similar escapade in August when he drove a car to a Belgium base, where he surrendered after being absent for 24 days. Sentence is subject to confirmation.