Hey there's a lot of readings of this thread showing (158) for the number of postings, does this mean these cars stop a lot?
While I'm here, I might as well hijack the thread now the original issue is closed and say I did have the 'engine stopping' thing a few years ago, it only did it coming up to a stop at road jucnction or traffic lights, never while driving like Damian's.
Why my engine stopped was because of a blocked-with-gunge butterfly throttle valve. Common fault with many cars. When foot is off accell pedal, throttle valve completely closes up, no air gap, shuts the air completely off. The Idle Speed Control (on the jag) is supposed to maintain an even tickover speed, but doesn't function at all when rpm below 500, so there's no 'pullup' effect and engine stalls. I'd found while car slowing down to a stop that if I declutched quite late, the engine rpm was prevented dropping below 500 and the ISC duly pulled up the revs and prevented the stall (by opening air valve as required), a useful tip to try if suspecting this problem.
When the throttle buttterfly cleaned out of gunge the Base Idle Speed became restored (just above 500 rpm), which is within ISC capture range. Of course if there's a different engine problem that's causing BIS to drop, you'll get the same 'stop' symptoms.
The fault can be hidden/compensated for by turning up the throttle stop screw to widen the throttle gap, (the one that's supposed to be set with feeler gauges according to manual).
Note that adjusting the allen key air screw in the ISC will make no difference to the BIS rpm, a common misconception!, all that does is set the maximum opening of the ISC air valve (the max amount of pullup).