Saxo stalls when accelerator is pressed

Help needed please; I have an “R” registration Citroen saxo mischief, (petrol). I know that it’s quite a few years old but has only done 59k miles, and want to fix it if possible. When I turn the ignition key it starts first time every time and idles at a nice speed, although if I touch the accelerator within the first 4 minutes of starting the car it will stall. If I leave it ticking over at its own pace on the spot for the first 4 minutes and then drive it, it’ll be perfectly fine and will drive like a new car! That is until I stop at a petrol station for instance and turn it off. When starting up again now that it’s nice and warm I get even more problems. The engine will just keep turning over without starting for approximately 1 minute of continuous trying. When it finally starts again we go back to the same problem as when cold start, and stalls if you press the accelerator. But as always once those 4 minutes of letting it tick over it’ll be fine again and drive perfectly until the next time it gets turned off! I get no warning lights at all, and the mechanics I’ve been to just scratch their head in puzzlement. This has been going on for nearly 6 months and its behaviour is consistent no matter what the weather is like. Please any advice or suggestions to end my torment!