I have just restarted re-reading Sandy Cavangh's book "Airborne to Suez". He mentions that they (3 Para) embarked on HMS "Theseus" to go to Cyprus (Famagusta) and then moved on to their base near Nicosia. He mentions that their Austin Champs went with them as deck cargo so the Champs obviously made it as far as Cyprus but it would seem that the RAF did not have the proper gear to attach them to a Hastings (at the time).
There is a photograph in his book showing a Jeep freshly delivered to El Gamil airfield still sitting on its platform. I'm sure you will agree that this is definitely a product of Mr Willys and not Mr Austin.