Toyota Yaris Verso; Repeated Intermittent Stalling - Help Needed

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I have a Toyota Yaris Verso 5 door hatchback 1.3, registered in 2000, bought secondhand in December 2006 with full regular service history and around 56,000 miles on the clock at the time. I have kept up regular servicing throughout and the car has been very reliable. First problem was encountered in 2012 with a warning light which turned out to be a faulty Lamda sensor, which was duly replaced. Warning light re-appeared and 2nd Lamda sensor was replaced even though it did not appear to be faulty. Warning light re-appeared but no fault could be diagnosed.

Subsequently the car started to stall on starting. The temperature sensor was checked; not working and was replaced. The problem remained. An air valve was also replaced as a possible solution. The problem remained. The external temperature or humidity has had no bearing on whether or not the engine will start and continue to run or simply stall repeatedly. It will start and keep going on a freezing cold, wet day and stall repeatedly on a hot, dry one.

After lengthy discussion and coming to my own conclusion that it must be the fuel cut-off valve at fault, I learned that the identical problem suffered by a friend on a totally different make and model of car turned out to be faulty wiring prior to the fuel cut-off valve. Repeated starting has never flooded the engine since this problem began, so I do suspect intermittent fuel starvation. Can anybody throw any light on this problem, please, as I really need to get this sorted!