JAGUAR S-Type - S-Type Misfire

Q
After three years of untroubled motoring in my 4.0-litre 1999 S-TYPE, the car has developed an engine misfire and no one seems to have an answer, including the Jaguar agents in Australia and New Zealand.
When the car first starts it operates normally until it returns to the idling speed. It will drop one, sometimes two cylinders. The only way to 'fix' the problem is to switch off and restart. I can leave home and travel any distance with no problems, it is only when I have to stop at an intersection or the like that the problem occurs. All coils and plugs have been changed, all electrics been checked, and there are no fault codes showing. It has been suggested that I get the camshaft timing on the driver's side checked as the plugs were quite black when removed.

A
A rough idle will normally be caused by a slight vacuum leak of some kind or, on high-mileage cars, worn valve stem seals allowing oil to work its way down into the cylinders. Alternately, if the roughness is only present when the brakes are applied suspect a perforated diaphragm in the vacuum booster.