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You could just put it on a spur from the double socket inside. If it’s only going to be a couple lights and a double socket that should be fine. You could either put plugs the lights or have another fused spur with a 3a fuse for the lights.
The slightly trickier bit is installing the armoured cable and terminating it properly to the sheath is earthed.This is based on the assumption that the garden room is close to the house and a suitable place for the cable to run. If it’s a long run or you want to put more sockets in I’d be inclined to put it on its own circuit like talked about before.
Hmm on this shed biz - if I want to get power to a ‘garden room’ do I need a new individual connection from the existing house consumer unit - through the house and out or is it possible to extend from a standard mains double socket position (by the back door) - which is on a general house circuit? Would be to run one or two led lights and a computer.