A few more clues from a Jaguar book:
"In 1953, Ian Appleyard foresook XKs, which were no longer eligible for the Monte Carlo Rally, for a Mk VII and finished a fine second in the general classification." I don't know if this meant that 2-seaters were no longer allowed or whether cars now had to be closed - I suspect it was 'no more 2-seaters'
XK 120s competed in the Alpine, the Tulip, the Liege-Sofia-Liege and the RAC so obviously 2-seaters were admitted to those events. They wouild have been in a separate class, probably with a stiffer time penalty than the saloons.
I have even seen photos of C-Type Jaguars running in the "Rallye Soleil Cannes' and the 'Tour de France'. As about 50 C-Types were made, they may have qualified as 'Production' cars.