The original fit on your X Type would have been Pirelli P6000J - the J denoting Jaguar. Sadly these are no longer available, i've used P6000s (the generic P6000 rather than the "J" type) on other cars and they've been really good tyres. I have a pair of (10 year old) P6000s on the front of my S Type and because of their age, their grip is reduced.
On the rear are (5 year old) P7 Cinturatos, not impressed with those either! I'm looking for a set of tyres to replace all 4 on mine but with yours being AWD, you'll have to renew all 4 at the same time with the same type all round to get optimum results.
There used to be a brand known as Corsa, these were old-pattern Pirelli tyres, made by Pirelli, i put a set of these on an old Volvo 740 about 18 years ago and transformed the car. I know with Jaguars in general, having the same type of tyre all round is more important than other cars but with any AWD/4WD it's also important to have them all wearing at the same rate to avoid transmission wind-up.
I'm currently looking at a set of :
https://www.ebay.co.uk/itm/144518219295
for mine, surprisingly good reviews for a "budget" tyre and not being impressed with the Pirellis (first time ever Pirelli have failed to impress me) they're probably a reasonable bet.
Will be interested to know what you finally decide on. 😉 😄