Some 90,450 children were living in temporary accommodation in the last quarter of 2014, a rise of almost 10,000 in a year, the statistics show.
The National Housing Federation called the rise "shameful".
The government said its changes were helping councils move families out of temporary accommodation more quickly.
The statistics, from the Department for Communities and Local Government, also show there were 2,040 households with children in bed-and-breakfast hotels at the end of last year.
Of these, 780 were in bed-an-breakfast accommodation for more than six weeks.
David Orr, chief executive of the National Housing Federation said the dramatic rise in the numbers of children "stuck in temporary accommodation like hostels and bed and breakfasts" revealed "the true cost" of not building enough homes in England.
"Often living in cramped and poor conditions, it's no way of life for a child and no way to help homeless families to get back on their feet and rebuild their lives.
"It is totally unacceptable that these figures are at a six-year high.
"Children are paying the price for the failure to build the affordable homes we need and will continue to do so until politicians take bolder action and commit to end the housing crisis within a generation," said Mr Orr.
Communities Minister Kris Hopkins said the government was working to ensure support was in place to help homeless families move on with their lives.
"Households now spend on average seven months less in temporary accommodation than at the start of 2010," said Mr Hopkins in a written ministerial statement.
Local authorities now had more flexibility to find "good quality, suitable and settled accommodation in the private rented sector", he added.
The government had also made it clear that the long-term use of bed-and-breakfast accommodation for families with children "is both unacceptable and unlawful", said Mr Hopkins.

Tony Tyler called for drone regulations to be put in place before any serious accidents occur.
He said the threat posed by unmanned aerial vehicles is still evolving.
"I am as excited as you are about the prospect of having pizza delivered by a drone," he told a conference in Singapore.
"But we cannot allow [drones] to be a hindrance or safety threat to commercial aviation," said Mr Tyler, director-general of the International Air Transport Association.
"The issue is real. We have plenty of pilot reports of drones where they were not expected, particularly at low altitudes around airports," he added. "There is no denying that there is a real and growing threat to the safety of civilian aircraft [coming from drones].
"We need a sensible approach to regulation and a pragmatic method of enforcement for those who disregard rules and regulations and put others in danger."
Drones were recently involved in four serious near-misses at UK airports, the UK Air Proximity Board said in January.
The board, which investigates near-miss incidents in UK airspace, said a drone had come very close to colliding with a Boeing 737 that had taken off from Stansted airport.
IATA's primary concern is drones flying at low altitudes near airports that could threaten planes taking off or landing, Rob Eagles of Iata said.
Aviation regulators also want to make sure that the radio spectrum used to control the drones does not interfere with air traffic control systems, he said.
In December the US government set up a registration system for Americans who own drones.
Anyone who has a drone must register with the Federal Aviation Administration before the device takes its first flight.
Owners have until Friday to register their details or face being fined.
The move comes after several reported incidents of drones hindering emergency services' efforts in fighting fires and other dangers.

They scored 428.91 to come second behind Chen Aisen and Lin Yue of China.
Daley, 21, and Goodfellow, 19, improved on their effort in the first round of the series in Beijing, where they picked up bronze.
Tonia Couch and Lois Toulson took bronze in the women's event, while Chris Mears and Jack Laugher won 3m synchro bronze for Britain.
Coach and Toulson's bronze followed a silver won in Beijing, but Mears and Laugher's success was their first medal of 2016.
The third round of the series takes place in Windsor, Canada from 15-17 March before the final leg in Kazan, Russia a week later.
The number of children living in temporary accommodation in England is at a six-year high, according to official figures.
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Drones flown by the general public are "a real and growing threat" to civilian aircraft, the head of aviation trade body Iata has warned.
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British pair Tom Daley and Dan Goodfellow won 10m syncro silver in the Dubai leg of the Diving World Series.