This is how the "donor" lamp (IKEA Slobo "owl" lamp) looks like in the inside.
The socket is a GUZ5.3 which is a polarity protected GU5.3. The inside round socket can be easily removed from the snap-lock, so you'll get a socket that's around 2cm in diameter.
The GUZ5.3 socket fits neatly in the original E14 socket with the wires pushed through the holes and soldered to the original lead. I have used a fair bit of hot glue to keep things stable:
I have used the original lamp lead and have replaced the connector with a fused UK plug (our native plugs are type F), so it's not possible to mistakenly connect this lamp to 230V. I have used the two main contacts (neutral and live) but thinking about it more closely, it would have made better sense to use the neutral and ground connectors for this type of hacked usage.