There is a channel on youtube called Fur Cough Classic Cars and they have a video posted for what they call "Jaguar XJ40 V12 Coupe Concept - M690CRW"
It looks wonderful but I don't know if it is a real factory prototype or some aftermarket job
Also if you watch the video you will spot a 2 door X300 convertible parked right next to the XJ40

Does anyone here know any more details about the history of these two cars?

 

The X300 Convertible is the "Daimler Corsica" (P300COR). Google for lots of info. A one off owned by JDHT.

If it ever comes up for sale I will consider selling my house to buy it (but I may still not be able to afford it).

 

Thanks for sharing. Very, very interesting. I have seen, in person, 2 door coupe versions of the Series III XJ6 so I would think this was a factory built project car. Either way, I wished Jaguar would have offered the XJ40s in a coupe version.