Garage wiring unsafe and not earthed

[Spoon]

Triple core what? If it’s armoured cable then the armour will more than likely be the earth, not the third core, it it has been glanded correctly

@Pete999 and myself have asked what type of cable it is. Just waiting for the OP to reply mate.
Also according to the OP none of the sockets or lights were earthed.

 

[Octopus]

Could that be dangerous as the local earth could be at a different potential to N? Or does it depend on the installation being check for that after install?

Your next step is to find a local friendly spark to come and determine what precisely is going on .......................making any further changes isn't a sensible course of action.