Welcome to the 1960s! The XJ6 uses an old Harrison (GM) A6 compressor. It's a beast. And it was used in probably millions of vehicles throughout the 1960s and 1970s (and 1980s, in Jaguar's case).
The business end of the A6. These o-rings are awful. This is either the source of a leak (could be since it was glowing with dye) or else it was more of a pain getting out than I remember.
After tearing down the A6, the front head had a broken reed valve. I couldn't find a new one and refusing to give up at this point, I resorted to the scrap yards and found a donor A6 to rip apart for the two bits that I needed.
As previously mentioned, the Harrison/GM/Frigidaire A6 compressor is about as common as it gets. A quick trip to one junk yard yielded several matching vehicles and it was just a matter of determining which was easiest to remove (from amongst the ones where the engine hadn't already been taken). This old Cadillac was the winner... if only the Jag's compressor was as easy to remove as this. I had it out in about 2 minutes.
(Skipping a bunch of time)
O-ring kits for the A6 are about $15 and it's easy to rebuild. I chose to install a more-modern double-lip shaft seal, which theoretically works better, though requires special tooling to install.
Skipping the entire rebuild process... there are plenty of photos out there and it's not convenient to take photos when your gloves are dirty and you're busy. The compressor was re-sealed and a new relief valve was installed. The appropriate amount of Ester oil was installed, as well.
(Skipping even more time)
At this point everything is back together. Before the hood went back on, the system was vacuumed and pressure tested (it held the vacuum for a week - that's a pass!). The hood was reinstalled and 2.5 pounds of R-12 was installed.
Cleaned up and ready for summer.