RepairPal Certified shops can diagnose and repair your 2002 Jaguar XJ8. They provide transparent pricing with a minimum 12-month or 12,000-mile warranty on repairs and services.
The 4.0l engine has en external oil pump. you have to remove the timing chain on one side, and then the oil pump can be removed and replaced.
This is a full weekend for a DIY project, but a few hours at the shop.