Fuel pressure problem

My 1990 XJS has about 55K on it and runs very well. When I start it, if I turn on the ignition and immediately crank on the starter, it starts but runs very rough, like it’s running only on a couple of cylinders. It seems like the fuel is not getting to all the cylinders. After 10-15 seconds it smoothes out and runs fine. On the contrary, when I start it, if I turn on the ignition and wait for 10-15 seconds before cranking the starter, it starts right up and runs fine immediately. I have replaced the fuel pump, the fuel filter and both fuel pressure regulators. That did not solve the issue. Any suggestions as to what the fix might be would be greatly appreciated.

That’s the standard fuel check valve symptom. You’ve already replaced the fuel pump, and the check valve is built into the fuel pump on the 80’s cars. When did Jaguar switch to an in-tank pump? Where is the check valve in an in-tank pump system?

Another thing it could be is a fuel leak. Most fuel leaks are obvious, but if it’s an injector sticking open it might not be obvious. Whassup with the level of the oil in the sump?