I have seen this twice now on a 2003 XKR and a 2003 XK8. Until the cars warm up, there is a slight bit of surging. It goes away after the cars are warm.
If you engage the cruise control when they are cold, it is most noticeable but even without that, you can sense it. It is not a big problem in fact many might not notice it.
No codes and no obvious ait leaks that I have found.
Any ideas?
Thanks

 

If it is surging only while in gear it seems similar to my 2005 XJ where it was torque converter. It was very subtle. Slight variance in RPM but consistent and noticeable by only regular driver. Mine was replaced under warranty happened about 60k miles.

 

@rothwell Ouch! Hope that is not the case. I believe it does it whether moving or not but I will check.
Thanks