Good luck - they are certainly not easy to find, but persevere, they are around.
I have recently (January and March) sold TWO of these I had spare to my needs.
I may have an extra jack that looks similar to the one pictured here. I’m not sure if there are significant variations, are there distinguishing features or dimensions I should check when I pull the jack out of the parts bin? My parts bin is aimed at late Mark V cars but occasionally an XK part gets under the tent and mixes with the stock (and the Mark V has many shared parts with XKs)
The correct Jack for an early XK120 (1949 > c Oct 1950) is as pictured, and is Jaguar Part No C.2953, albeit this C.2953 is retained for all the later variants of this Jack as used on XKs up to 1960 that all have a welded-on square-tube lifting arm (and other differences)
But yes, late Mark V also used this same identical C.2953 Jack as per the pictured one, indeed I have no way at all of knowing whether pictured Jack is originally ex-XK120 or ex-late Mark V.
Earlier Mark V Jacks, part number C.2654 vary in a number of areas, and are NOT correct for any XK120.
The characteristics to look for, is the overall-length of the main tube.
The swaging-arrangement (indented groove) at the top-end of the tube.
The Hexagon-Size of the Driving-Nut at top of Jack.
The lettering on the top of the cast foot, and indeed often there is a mm/yy date stamped underneath.
The very-characteristic CLAMP on the tube, to hold the lifting arm - and its adjustable position on the tube.
And most importantly the correct ‘H’ section lifting arm, its length, and the angle of both ends - that allow for the angle the arm sits at, with a couple degrees movement only possible on its pivot-bolt.
But if you do have a correct late Mark V Jack, all the above detail will be correct.
If you have a similar STEVENSON or SMITHS STEVENSON Jack as supplied to other than Jaguar (all manner of other British cars received STEVENSON Jacks), then all the above characteristics will determine exactly what make/model of car it was supplied to, bearing in mind STEVENSON Jacks were first introduced in 1936 (thus evolving manufacturing characteristics), but offered in a variety of lengths, and a variety of Lifting Arm arrangements
I have one meeting the exact specifications in Roger’s post. It is perfectly functional and I am presently using it as the jack in my newly restored 1959 XK150S FHC. It is date stamped 1/49 on the base. I acquired it while I owned XK120 Alloy 670005 which had been constructed in June 1949. It is now surplus to my needs.
It’s been great that my post generated so much enthusiasm to find the period correct Jack. There were two correct Jacks available, one from a UK dealer and another from a dealer in the US, both for what I considered very high prices.
Roger McWilliams, seeing my post took a look in his garage and found a jack marked under the base 9/49 and fitting the description of the jack Roget Payne described. He made it available at a very reasonable price and I now gratefully have that part of my search sorted out.