Rough runnng then stalls

!y 92 cabby gti has a little issue…
It starts eventually after 3 or 4 seconds and a few spins of the engine and ticks over from cold at around 1500rpm. If you leave the car a minute before driving off there are no issues. However when you set off straight away and then come to a stop the revs drop and the engine eventually stalls. It only does this when the engine is cold.
Once warm there are no issues with running but it does seem to be running rich……it then take a long time to start. Usually 5-6 seconds.

The car has had new leads but I'd rather know what the issue is before I start replacing things that are ok.