London councils are increasingly uprooting homeless families with school-age children to house them outside the capital, according to figures published by the Green party.

Figures provided by 23 councils showed the number of families they are placing in homes outside London has risen tenfold, from 21 in 2010-11 to 222 in the current financial year, and with 10 boroughs not returning data the total is likely to be higher.

The figures, which were provided following a Freedom of Information request, underline the pressure councils are under to find homes for families, as social housing has been sold off and private rents in the capital have rocketed.

Of the boroughs that responded to the party's request, Brent was the council that housed most families out of London, moving 49 from the capital in 2013-14. It was followed by Greenwich with 38 and Newham with 28.

Between 2010 and 2012, Newham did not move any families out of London, so the figure is a big jump. In October, it emerged that 29 young single mothers had been told that they could be rehoused as far away as Manchester, Birmingham and Hastings after the council cut funding to a homelessness hostel.

The Greens also asked councils to report on how many households including school-age children were being moved out of borough, and this figure has also increased, from 1,428 in 2010-11 to 2,687 this year.

The group's London assembly member, Darren Johnson, said: "These figures show that the mayor isn't keeping his promise to families with children.

"He is looking the other way while hundreds of children are moved away from their local schools, their parents separated from local support networks and possibly made to lose their job. It shouldn't take freedom of information requests to put the spotlight on the suffering that is happening under his nose."

The homeslessness charity Crisis described the figures as "shocking" and said they only showed part of the picture of people being forced away from their communities.

Its chief executive, Leslie Morphy, said: "These shocking statistics are a direct result of cuts to housing benefit at a time when rents are high and there is a chronic lack of affordable housing.

"Worse still, they only take into account those who councils have a duty to house – single people not considered in priority need are likely to be even more vulnerable to homelessness and having to live a long way from their roots.

"Forcing people away from their communities, friends, families and support networks will leave them isolated and with even less chance of keeping or finding a job."

Councils across the capital have been struggling with growing housing lists, and many have taken advantage of new rules provided by the Localism Act which allow them to remove large groups of people from their list, including homeless residents.