Hi Bidr,
Thanks for posting his service book and discharge certificate. Unfortunately, as you say they don't provide much in the way of clues to his regiment. Except one possible one. On the Particulars of Training page, it states RAC (Armd). The Royal Armoured Corps has two main components, the reconnaissance troops and the tank regiments. Armoured in this context seems to show he was in a tank regiment rather than a recce regiment. However that may be a false conclusion.
The
Royal Armoured Corps was a really big organisation and consisted of the traditional 'Cavalry' regiments such as the 8th Hussars or the 12th Royal Lancers, the Yeomanry Regiments (TA soldiers) and the Royal Tank Regiment - which confusingly was itself made up of a large number of battalions, later to be renamed Regiments. At the height of the war there were over 50 RTR battalions, but at the outbreak of war, the RTR consisted of 20 battalions: 8 regular and 12 territorial. Your grandfather could have served in any of these regiments.
The other thing to note is that his trade in the Army was MT (mechanical transport). This could mean that he drove the trucks that accompanied the tanks, carrying things like additional ammunition, spares, water, rations and fuel for the tanks themselves. However the Particulars page also notes he took part in a preliminary gunnery course, which implies being trained as a tank gunner. I can't read the next entry which ends in -lifting. I think that had he been part of a tank crew his trade would have been listed as something like gunner/loader, driver, or radio operator.