Beany ........ any cables running into the garden must be protected by an RCD (earth trip). If you have an older system with no RCD protection, then use a plug that has one built in
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Bare conductors with no RCD protection are a danger to anyone nearby...... not only the rabbits.
Armoured cable would be better. If not that, then shove the cable through metal conduit. A piece of steel water pipe, or even a length of copper pipe is better than nothing.