P1111 is not a fault code. It is a special designator Jaguar uses meaning system ready, drive cycles completed after the last fault event. P1000, on the other hand, means system not ready, or drive cycles not completed after the last recorded fault event.
Some OBD II Basics - All P0xxx codes are generic and uniform across all manufacturers and mean the same on every car. All P1xxx codes are manufacturer specific codes. You cannot use a generic code chart to analyze P1xxx codes for a Jaguar.
Next time your car displays an engine fault light, try reading the codes then. If you have a CEL illuminated and the only code read is P1000 or P1111, then you probably have a fault that generic code readers cannot see. Could be a chassis code, for example.
One last thing - Neither P1000, nor P1111 can be erased.
Hope this helps you.