No doubt it’s women. If the design is a few years old they have to change it. 
Here is my oval base. It is cast aluminum and chromed.
That red/orange sleeve seems to be original, near as I can determine. There are a couple more in other places on this car, like the ignition coil.
There is a curious angled slot in the socket, as if you could turn it to disconnect the center contact from the bulb contact. In fact I found it was turned, which was why the bulb didn’t work.
Back to the original question. Here is the info from the Mark V SPC.
You could search for Lucas 31185. It’s a very short stroke device. A long stroke wouldn’t work in a tool lid like it does with a passenger door.
Worcester Classic Spares doesn’t list it, but they might be able to get a used one.
Or there is Paul Beck Classic and Vintage Supplies.
Coventry Auto Components has the long one. They might know about the short one.
This subject came up on the XK forum a couple of years ago.