Hi there again,
How long has it been since you replaced the diaghram in the carburetor? I'm refering to the rubber diaghram that operates the slide valve, it's about 4" in diameter, and MUST NOT HAVE ANY HOLES IN IT. They only cost around $6.40 here, and I replace the two on my Jag yearly, just to be safe. They have to be in good shape to allow the slide valve to rise. If it doesn't rise in response to the vacuum increase on the intake side of the slider, the car will run VERY rich and will have NO response - it will hardly go above an idle, or in your case it might even die due to running too rich.
One time when I needed one in a hurry I made one out of a piece of thin player piano cloth - they cloth I used was left over from recovering our reproducing grand piano pneumatics, and was nylon cloth reinforced neoprene, probably was a better quality fix than the factory rubber.
By the way, be sure not to overfill the oil resevoir, the excess oil ends up on the rubber and causes it to deteriorate. I always use Marvel Mystery oil in the resevoirs at the direction of the Jag factory manual.