Stalls. Starts sometimes

1997 XJ Sport recently stalled a mile from home & wouldn't start up again. Engine cranked, but no ignition. Replaced battery a couple days later and XJ started rough on 2nd crank. Drove to another location to change oil. No start again... left at location and started quick a couple days later, yet bogged out when given throttle.

Basically, XJ starts when it feels like it & now threatens to stall at any moment. New battery charging fine. CPS changed out several years ago(?) Idles also sometimes jumps when reving engine in Park. Previously idled fine for years...

My mech. thinks now it might be fuel pump... Any thoughts or similar symptoms?

Do your checking. Fuel pressure, spark, compression. Sounds like it could be afuel pump but thinking it might be something and knowing what it is can be the difference between a little and a lot of money. Check your fuel pressure key on engine off, running, and check for how quick it drops after key off.