You may struggle to get the exact part, which may be made from  Chinese unobtanium on a mass produced lamp, but single hole mounting plugs, sockets and other parts like  rocker switches are very common.

To help searches, if the nut is on the outside it is often called 'jam nut' fixing and the part can be fitted already wired up. If the nut is inside it is considered panel mount, as the either wiring or the fitting has to be threaded onto the panel before wiring can be completed.

Is it mains, or ELV. ?

If mains and you need to get it going in a hurry,  you may be able to convert the thing to a fixed cord with a stuffing gland and some flex with a plug on it...

If you know the hole size, the contact pattern and the depth in front and behind it should be straightforward to advise. No marking on the body I suppose ?

A photo of the contact face may help eliminate some.

Mike.

Hi Mike,

There is nothing on it at all. I've attached some more images. The back nut that holds the gland in place is located inside the lamp itself. 

OK, well now I'm more confused. So what do we see looking at either end you call it a connector but - is it a plug, a socket, tunnel terminals with two lots of screw terminals or what ?

Photos of the connector faces really would help.

Or are you just after a nut for the end on the left in the photo?, when threads per inch and hole diameter would probably allow a thing to be identified . Looking at the finger or scale it could be PG9 thread. Or your fingers may be bigger than mine..

OK, well now I'm more confused. So what do we see looking at either end you call it a connector but - is it a plug, a socket, tunnel terminals with two lots of screw terminals or what ?

Photos of the connector faces really would help.

Or are you just after a nut for the end on the left in the photo?, when threads per inch and hole diameter would probably allow a thing to be identified . Looking at the finger or scale it could be PG9 thread. Or your fingers may be bigger than mine..

The picture on the left shows the connections for the main power cable from the mains and the picture on the right the few inches of connecting cable coming from the lamp. Very straightforward. The image on the right shows the thread that snapped off, that the back nut within the lamp screws to hold the fitting in place, you can see it better in the pictures I sent yesterday. 

So, this looks like the one on an LAP outdoor LED lamp I had at home. Possibly manufacturer-specific and I think the replacement for that particular range now comes with pre-fitted flex ?

Ah! a picture paints 1K words and all that.

now the really sad admission is that after 30 years or working in the electrical and electronic arena, preceded by a further 10-15 years of playing with it first as a school kid and then a teenager, I'm not really sure what you should call that either.

But I do wonder ff a more normal gland without contacts, and some crimps or wagos, perhaps aided by a conduit joiner to free up some space, could be pressed into service as a replacement.,

Mike.