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Just taking off a wheel and a nut has sheared. I don’t mean the thread stripped, the nut actually broke in half. Half is still on holding the wheel in place but it’s the part with no hex to put a socket on.
Get a 19 or 20mm hole saw, remove the drill bit & the saw will cut through the nut to enable you to remove the wheel.
Then you can remove the remainder of the nut with grips.
This should not cause any damage to the wheel or stud!
I recommend you swap out all 20 of those sorry sheet metal covered lug nuts. Replace them with a solid version. Stainless steel is even better but just chrome plated steel ones are cheaper and won't distort and get stuck on the hub. We have dozen of threads where the cap failed and left people in your situation. Yours is the first time I have seen the lug nut shear off that way.
Surprisingly Jaguar has been using these sheet metal covers for well over 20 years. I have had 2 Jaguars and one of the first things I do is get the solid lug nuts installed.
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Well that is because you purchased the wrong aftermarket lug nut??
The ones I got are an exact copy of the crappy sheet metal covered factory ones. Mine also take the same size lug wrench. You might also take a look at the sorry lug wrench supplied by Jaguar too. Many have upgraded to a 4 way wrench.
Here is a basic search on this forum for lug nut problems; Lug Nut Problems
Just be aware of above when purchasing replacement nuts.
It is true that the solid nuts shown are 4mm longer than the factory nuts, the important measurement is the thickness of the wheel boss through which the nut fits. My 2012 XF Portfolio (X250) is fitted with 19" Caravela wheels, the boss is at least 14mm thick so these nuts will tighten just like the factory nuts and are safe. It makes sense to check any none factory wheel nut for fit with the wheels you plan to use to ensure the nut will tighten against the wheel.