This is the correct tool to open the spare tire compartment and remove the rear spats.
But it was only used on Mark V, no other Jaguar model, so it is hard to find anymore.
Alternatively, you can use the Tee Key or Coach Key now offered by many suppliers.
The jacking sockets on the Mark V are very strong, assuming the chassis is not rusted away, and I have used them many times with the correct jack in my younger days when I had no other.
The scissors jack you have is what my modern S-Type and Volvo have, not intended for and will not fit the Mark V as is. If you really wanted to carry it for emergencies, you could flatten out the saddle or remove it, and just put this jack under the frame near one of the rear jacking points. But it really is not a very good jack, rather unstable, and I would only use it for changing a flat in an emergency if I had no other jack and I was on flat solid ground or pavement and had wheel chocks and put the gearbox in first gear.