Those with children already attending nurseries not on the list - only a few hundred yards from home in some cases - are asking headteachers if this means the children will have to move.
As the families of half the 12,000 children covered by the Government's pilot voucher scheme received their lists this week, an embarrassed Department for Education and Employment explained that the culprit was a bug in the computer at Capita, the company administrating the pilot scheme in four local education authorities (Norfolk, Westminster, Wandsworth and Kensington and Chelsea).
The computer generates a separate list of choices of nurseries in both the maintained and private sectors for each family with a four-year-old child. It selects the 40 approved providers nearest to each address by matching postcodes.
A check of the system following the first complaints from schools whose nursery classes were not on the list has revealed that whenever the computer programme found two providers the same distance from the family's address, it responded by dropping one of them.
Capita has told angry heads who have telephoned to complain that revised lists will be sent out.
Michael Day, the DFEE official responsible for the scheme, said that schools were more likely to be missing from the initial list because they had not applied in time. But he conceded that this could not be true in the three London LEAs, who had each sent in their schools on one list.
Nevil Coulson, Westminster's deputy director of education and leisure, said the council had received complaints from four schools as soon as the lists came out and that a good many more might have been affected.
One missing school was St Peter's primary in Eaton Square, whose nursery class is over-subscribed. Head John Wright said: "It has been very disturbing. People are bound to ask why a school whose nursery provision has been so highly commended by OFSTED is not on the approved list."
Angela Piddock, head of Wilberforce primary school on Westminster's deprived northern edge, which was also left off the list, said: "Parents were worried and I was furious. We're oversubscribed in the nursery department, but if we lose rising fives in the reception class than it is likely to affect our future roll."
The second batch of parents will receive their lists later this month.