Sean, yes it's steel bodied.
There was a wooden bodied one being repaired somewhere in Northants a couple of years ago which was used as a recovery truck at Silverstone race track. I haven't heard anything about it though for a while.
I remember seeing another wooden bodied one at a scrapyard in Watford in the early eighties which was later bought and restored by a chap who ran an Army cadet group. He used it for towing a 25 pounder and used to park it in Berkhamsted, but I last saw that one about ten years ago.