I know this is a year old, but I've got to the bottom of this. I now own this car (Eddie Shaw's name is in the service history, so it's this car). When I bought the car I did some searching to find the answer and this unanswered thread (and another one from the guy I bought it from) are the only XJS specific ones. Nobody seemed to have encountered this problem before, so I'll answer it just in case anyone else runs into it.
I found that when I put my hand on the Oil cooler inlet pipe (passenger side), I could feel vibration very strongly. I put a screwdriver on the oil cooler and heard the noise through it very loud and clear. The oil cooler fitted was not the original, it was a pretty poor quality aftermarket copy made by a company called Oxford Coolers. It didn't mount correctly and the mountings were all thin and damaged. The decent ones have a solid bottom with a tapped thread, but this one had a thin folded over piece of sheet metal welded to it with a nut and bolt, and it'd snapped. I'm not sure when the oil cooler was changed last time or why, it is not mentioned in the service history. At any rate, it must have had some kind of restriction form internally, causing the noise.
A new oil cooler, set of pipes (because they weld themselves to the cooler) and an oil change later and it's quiet as a mouse. Well, a V12 mouse.
I will say though, someone who knew what they were doing had been in there at some point. They had installed flashing tape to plug the gap between the oil cooler and AC Condenser, which is a reccomended thing, and all the foam around the radiator was intact and spot on.
