REME was formed from these -
RAOC (Engineering Branch, admin and storemen of the Royal Army Ordnance Corps)
RASC (Royal Army Service Corps, Heavy Repair Sections)
RE (specialised workshops of the Royal Engineers)
So could he have been in one of those?
You could try posting a question on the Armed Forces board to see which would be the most likely. They are very knowledgable on there.
Betty