There is also one other possibility, if the fuel injectors are bad it many timed mimics a sensor problem. See last entry this post =

https://www.jaguarforum.com/showthread.php?t=56815

 

There was also a change some time in the past of the connection to the sensor. The contacts (per Jag) were not letting correct voltage through and there was a change made to the connector that had more gold in the contact connection to allow better throughput.

 

Iirc, the old connector was black and the replacement was gray. Going by memory here of reading about this months ago.