My 2007 3.0L S-Type has 19mm lug nuts, yet the wrench in tool kit that appears to be the original is 22mm. Is this the wrong wrench or have the lug nuts been replaced? The wrench is marked "R8A-17032-AB Jaguar D3L5A 2406"

 

Post a picture of each.

 

So here is the picture

 

Not sure what purpose the picture served but anyway I'd guess your nuts have been upgraded. That must be good? I foresee a new wrench in your future.

 

Actually I don't like these nuts. They bind real tight even if they are done up light by hand. So can you tell me the original OEM nuts and I may get them

 

The original lugs are 19mm head (with thread 12mmX1.5mm) and they are not worth keeping. They are ordinary nuts with a sheet of SS covering them and they are a real pain, as they slip and deform, they are plain useless! The original wheel spanner is of the same quality, or rather- lack of same!
The wheel nuts should be lubricated with a bit of grease and tightened by hand, not lightly and not forcefully, but with a good tug. Remember it might be yourself that has to take them off on an empty stretch of road.
No nut will go tight, if the thread is right and the nut fitting for the purpose, with an exception of SS nuts, that fret sometimes for no good reason.

So inspect the lugs and see if they are right for the use, thread, hole, washer etc and be glad, if they have been replaced with ordinary type lugs.
And then get a spanner that fits!

 

Those look like the original nuts and an incorrect wrench. The 19mm nuts are known trouble, I'd replace them. There's slots of discussion about suitable alternatives.

 

Jaguar insist they NOT be greased. If you do grease be sure to reduce the torque!