It may not be relevant but the Allard Palm Beach II could be Jaguar-powered, so the puzzle car could have been one of those re-bodied.
If it was a rebodied Palm Beach, surely the vendor would have said so in his advert as it would hve made it more saleable.
The choice of name, Jaguar-Allard, suggests to me it wasn't simply an Allard chassis with a Jaguar engine fitted, which would have been called an Allard-Jaguar, but a special with a Jaguar engine fitted in a modified Allard chassis. Hence the description "Especially built for sprints and hillclimbs".
But this is all mere speculation.