The car should of had a rear diff oil change at 4yrs old. It will be very obvious if it has or not by the quality of the oil that comes out now.
Firstly open a case with the dealer with the after sales manager.
Secondly open a case with Jaguar Customer Relations. Explain that Jaguar have failed to keep to the maintenance schedule of the component for the service you paid for resulting in premature wear and put the emphasis on them to prove otherwise. With a well worded letter you should get a loan car and usually 90% of the cost paid for if not 100%.
It all depends how you approach the situation and terminology and words used. Friendly but harsh assessments showing failure tend to work best.
For example I had both lower control arms changed for free at 4+ years old because one was worn and appeared as an advisory on the MOT. My discussions were around quality of components on a 80k 174mph vehicle after just 32k miles and invited them to inspect it. Parts magically appeared and they covered 100% of the cost plus 4 wheel alignment and loan cars within 2 weeks.