I have a 2003 Jaguar XK8 4.2L
Most of the time when the car hasn't been started for a day or two it will start up on the first crank, when the car has been running and warmed up, I can sometimes turn the car off and then restart oh, but it will take several cranks of the engine before it will actually start the car.
According to the documentation that I have, a new fuel pump was installed before I became the owner.

Does anybody have any ideas what I should look for to fix this problem?

 

When you get the long start does it stumble a bit and act like the engine is starved for fuel?

Could be the small check valve in the pump that is intended to prevent fuel draining back to the tank. The fix would be to replace the pump assembly but the design is not very good and there is a tendency for the issue to come back over time.

Mine does this and I’ve just come to accept it as a quirk. Cycling the key a couple of times will “pump up” the fuel system and once the pump is running continuously after starting there are no issues.

 

Yes it does stumble like deprived of fuel.
I thank you for this info and I'll be sure to try your trick.

 

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