Somehow I've ended up with a locking wheel nut key that doesn't fit the nuts on my Jag.

Does anyone know how to determine the model letter so I can buy one?

Yeah; the dealer, but they're literally miles away and will likely want one of my nuts in exchange 🙄

I have just encountered a similar situation, however a "friendly" mechanic managed to lose mine key completely!

If you get really stuck and don't want to go to the dealer, get a cut off tool and cut a slot in the top of the locking wheel nut dome. Using a cold chisel and a big hammer, you can then shatter the dome. This gives you access to the stud, which can be removed using stud removers from Machine Mart. 

I don't think the dealer will be helpful - the last I heard was that there is no real way of identifying the locking wheel nuts on the X-Type. I did the above trick on all 4 wheels and fitted normal nuts.

That's likely how I've ended up the a key that doesn't fit.

Had a puncture repaired a while back and they used the correct key to get the wheel off. I immediately popped it into one of the cup holders, which is where the wrong 'un is languishing.

I'll just have to break out the mini angle grinder.

Ta very glad.