Easy one this! no YOU can't do any wiring out doors legally, needs a 'Part P ' full scope leckie to do any fixed wiring outside, thats law.
He can fit IP rated Switched fused spur next to socket and connect lights to that, or if really being'Tight' you could run from socket with plugged in flex as now but run flex via waterproof switch in line using proper flex glands, at least you would have protection of 3Amp plug fuse, not recommended but......
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