For a start it depends on if the armour actually requires an electrical termination or mechanical restraint at that point. If not it can simply be dealt with like any other cable, such as T&EBut what concerns me more is that brown/black/grey usually indicates an armoured cable, armoured cables are usually terminated with a gland that restrains the cable and earths the armour. It sounds like this installation may have been a lash-up from the start and is in need of some remedial work beyond reconnecting the grey wire.
I'm assuming the earth sleeved black at top right is the 3rd core and hope the armour is earthed at it's source.
One situation where the SWA gland caused a hazardous situation
My solution to removing the hazard:

