Thousands of private nurseries are declining to accept two-year-olds from poor backgrounds, despite a £100m government initiative to extend childcare to the most deprived families. The revelation has prompted concerns that some nurseries do not want poorer children mixing with those from middle-class families, their core clientele.

All three- and four-year-olds receive free early education, but the extension of free childcare to some two-year-olds is not universal; instead it is specifically aimed at the underprivileged. The government pledges that from next month 40% of the most deprived two-year-olds – 277,000 children – will be eligible to receive up to 570 hours of free early education a year, equivalent to 15 hours a week for 38 weeks.

However, figures released under the Freedom of Information Act indicate that 44% of local authorities did not have sufficient places at the start of this year. It is estimated that 63,000 two-year-olds are on waiting lists, while many councils are not expected to have sufficient provision until the second half of 2015.

The problem is acute in certain cities: in London, only 45% of the eligible two-year-olds have a place. The borough of Lambeth now has a waiting list of more than 1,000.

The initiative has hit problems because it appears many private and voluntary nurseries, which provide the vast majority of places, are reluctant to embrace it. Of the 25,547 nurseries and pre-schools in England, only 13,685 have opted to offer free nursery provision for two-year-olds, compared with the 18,960 open to three- and four-year-olds.

"There are a number of different reasons why childcare providers choose not to offer free places for two-year-olds, and social mixing is a consideration," said Anand Shukla, chief executive of the Family and Childcare Trust, which is campaigning for universal free childcare for all two-year-olds. "As well as benefiting two-year-olds with free early education and providing additional support to working parents, a universal offer would remove such stigma."

Research carried out by the trust for London councils found that "some providers felt that some of the working parents in their nurseries and pre-schools would object to large numbers of vulnerable children being admitted to their setting and that the 2013 cohort of children would not 'fit in'".

Other organisations said the funding arrangements made taking poorer children economically unviable. The Department for Education offers £5.09 an hour to local authorities to deliver free early education.

The National Day Nurseries Association claims that a "chronic underfunding" of universal free childcare hours is "making it impossible for high-quality nurseries to provide the places affordable to parents". As a result, a significant proportion of two-year-olds from deprived backgrounds are ending up in substandard nurseries.

Department for Education statistics show that 13% of two-year-olds in England are being placed in provision that "requires improvement" or has failed an Ofsted inspection. In some local authorities the percentage is considerably higher. For example, a third of two-year-olds in both Lewisham and Salford are not in nurseries judged to be good or outstanding. This is a concern to experts: evidence shows that only high-quality early education can narrow the gaps between the poorest children and their peers.

Concerns that nurseries are becoming havens for middle-class children echo comments made in April by the chief inspector of schools. Sir Michael Wilshaw warned that the preference among middle-class parents for children to engage in play over education while at nursery was harming those from poor backgrounds who would "benefit hugely" from the chance to learn.

"The chattering classes will never have many problems in bringing up their children and finding the best ways to educate them from the earliest age," Wilshaw said. "This prejudice prevents us naming the problem, let alone tackling it. Some children are taught. And some are not."

Labour MP Lucy Powell said she would be tabling a series of parliamentary questions to gauge the true extent to which private nurseries were opting not to offer free places to two-year-olds from deprived backgrounds. "The policy of offering up to 15 hours a week free nursery provision to the most deprived two-year-olds is a good policy," Powell said. "But it has been managed very badly by the government. They need to understand that they must do more."

A spokesman for the DfE said it had made money available to councils to ensure all children received "the very best start in life".

"Councils must ensure that every eligible family who wants a two-year-old early learning place receives one and we have provided £100m for councils to invest in new buildings to ensure they meet this demand," the spokesman said.