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A metal appliance, connected to the mains, NEEDS to be earthed. It only needs a stray strand of one of the wires to contact the frame and it has a 50% chance of becoming live. Or the cable insulation can get chafed through, over time. For safety's sake you need to use a three-core mains lead and connect the earth wire to the copper pipework and the body of the lampholder. A strain-relief where the mains lead enters the base would also be a good idea.