Thinking on, there was a lorry mounted brigade in the division, and I think there was a backtrack mounted battalion in the tank brigade. Which would explain their presence at Villers Bocage.
Having looked into this a bit more, I have remembered reading that 7th Armoured Division and 11th Armoured Division both paired armoured regiments and infantry battalions in the Second World War. This appears to have been a divisional decision rather than doctrine. By the time of the Normandy landings, each armoured brigade within an armoured division contained a motorized infantry battalion mounted in half-tracks. The doctrine called for one company to be attached to each armoured regiment.
Given this, and what we've discussed about the 70s onwards, I think it is reasonable to assume there was formal all-arms task organisation in the 50s and 60s.
I must hit the books, it's been too long since I refreshed my memory.
Edited by Stuart Galbraith, 24 August 2019 - 1147 AM.