Here in the US you can simply get a cord set with a single clip-equipped C7 socket on the end for such a purpose (there's also three socket versions for multiple/larger creations)
... And so we can in UK (and other European countries). Ours have an E14 socket, rather than your E12 We British have a BIG problem: compared to your dainty E12 sockets, our E14 sockets are gigantic. This is because of our higher mains voltage and consequently more stringent safety regulations.
Jen is much better going down the battery powered route rather than having to build a much bigger glitter house!
