Almost 20,000 children are spending the night in homeless shelters in New York City, according to new data, an increase of 24% since July 2011.

The Coalition for the Homeless, which published the figures, said the number of children in shelters would be even higher were it not for the fact that 65% of homeless families seeking admission to shelters are being turned away.

The homeless charity places some of the blame on the closure of the Advantage housing program in the summer of 2011. Since then there has been no rent-subsidy program in place for accommodating homeless families.

The number of homeless children in NYC shelters rose from an average of 15,704 in July 2011 to an average of 18,489 in July 2012, the most recent month for which average statistics are available. A freedom of information request by the Coalition for the Homeless found that 19,537 children were in shelters on 23 September – the most recent information available – which it described as "an all-time record high".

"For the first time ever there is no program in place to help people move from homeless shelters to housing," said Giselle Routhier, a policy analyst at Coalition for the Homeless. She blamed mayor Michael Bloomberg's administration for the increase in homelessness among children, the impact of which she said is "really detrimental".

"Homeless kids are more likely to feel anxiety and depression and an array of other health problems. That impacts itself on schooling as well – homeless kids miss more days of school, oftentimes they do worse in school than their peers, so we know it has a very negative impact. The fact that we're seeing record numbers of children in shelters is very disturbing to us."

The data show that so far in 2012, only 35.4% of families applying to stay at homeless shelters were admitted, meaning almost 65% of families attempting to stay at shelters are turned away. In 2007 51.9% of applicant families found shelter.

The Bloomberg administration opened nine shelters in June and July in response to increasing demand, and plans to open five more before the end of the year. Earlier this summer the New York Times reported that the department for homeless services, who have not yet replied to the Guardian's requests for comment, acknowledged that dropping Advantage in 2011 had had an impact on the number of homeless people. The city said it ended the scheme, which provided rental subsidies of up to $1,000 a month for two years to homeless people who found jobs, after the state withdrew financial support.

But Routhier said that the number of children in homeless shelters was rising even while Advantage was in place, as "a large number of families" would be forced to move back into shelter after the two-year subsidy ended.

"It wasn't a real permanent solution to move folks out of homelessness. To us, the real solution is providing permanent affordable housing resources, that is something that had been done prior to 2005, where existing affordable housing resources such as public housing and Section 8 were allocated to homeless families in shelter, and right now that's not the case."