Hi James and welcome to the club.
The Diesel engine in the XK is a slightly improved one and is similar ro the 2.7 diesel in the S type and earlier XF. Tell the dealer that the diesel engine has a belt and the petrol engine has a chain.
You could also tell him that there is no charge for that information,
Regards,
Peter.
I wonder if it could be a worn suspension component but it should show up with a lever bar inserted into the correct places to show excessive movement.
Other areas to look at could be loose / excessive play in the calipers where they mount to the carrier, worn wheel bearings, testing run out on the discs in-situ, etc