Green’s Dictionary of Slang

1. the act of stealing a vehicle.

1990

Oxford Times 27 July 15/2: Twoc – to rhyme with ‘clock’ – is police shorthand for the offence of taking and driving away a vehicle without its owner’s consent... From the victim’s point of view, ‘only a twoc’ has a very hollow ring to it.

2. a vehicle that has been stolen and driven illegally.

2005

B. Hare Urban Grimshaw 73: Got to torch the twocks, Chop. Fingerprints.