The number of households being moved out of London by councils has increased dramatically, rising by almost 50% in the first half of this year as town hall leaders blame rising homelessness, tightening public finances and a chronic lack of new cheap homes in the capital.

Councils have sent homeless households as far away as Glasgow, Newcastle and Cardiff in the last year, according to figures collected by local authorities and seen by the Guardian. Seven hundred and 40 households have been relocated to Kent, 574 to Essex, 30 to the West Midlands and 69 to Surrey.

More than 1,200 households were sent out of the capital in the first six months of this year – a 46% rise in the number of out-of-London placements. Six hundred and eighty-eight households were sent away between April and June alone, the highest rate in at least six years, up from 113 households in the first quarter of 2012-13.

The details of a sharp rise in a practice that critics say turns families’ lives upside down emerged on the eve of the budget in which councils have called for the chancellor, Philip Hammond, to stabilise their funding, which is on course to have been cut by 63% between 2010 and 2020 – a reduction in real terms of more than £4bn.

“Losing your home is a deeply traumatic event and then being offered accommodation miles away from your community, your work, your children’s school and your care responsibilities compounds all that trauma,” said Karen Buck, the Labour MP for Westminster North, whose constituents are regularly forced to move away when they become homeless, often due to families expanding or children growing up and needing their own places. “People are struggling against the most appalling odds to hold their own lives together and above all to hold their kids’ lives together.”

She said it was almost impossible to get a local housing offer for her constituents.

One mother of a 12-year-old and 14-month-old baby who was recently moved away told Buck she had to wake her family at 5.40am and spend more than two hours travelling to her work and her daughter’s school in Westminster. They got home after 9pm having commuted in total for four hours and 51 minutes.

“My kids were so hungry and tired,” she said.

Councils have struggled to locally rehouse people who present themselves as homeless partly because social housing is full and the amount people can spend on private rent under housing benefit has been been frozen since 2015 even as rents have risen.

Shelter said the figures were “a damning indictment of our housing system” and “show just how desperately we need more social housing”.

“We see people having to quit jobs, drop out of education and move hours away from friends and family,” said Greg Beales, the director of campaigns at Shelter.

The problem has begun to spread to other cities. Over the last five years, Birmingham has placed nearly 2,000 households beyond its boundaries, while Liverpool has moved 82, according to responses to freedom of information requests made by the website Huffington Post.

Darren Rodwell, the council leader of the London borough of Barking and Dagenham who speaks for London councils on housing, said: “We want to be able to keep people near their jobs, schools, and communities, and to avoid bringing even more upheaval and uncertainty into their lives. The best way to reduce out-of-London placements is to reduce homelessness in London. This means the government fixing the flaws in universal credit and reviewing the impact of its welfare reform policies as a matter of urgency. It also means properly empowering London boroughs to build new council housing at significant scale.”

Almost 70% of all of England’s homeless households are in London. Councils have an obligation to find them homes, which can sometimes be for only a few nights. The majority of those re-housed beyond the capital are families, it is believed.

Labour’s shadow housing secretary, John Healey, said the figures were “shameful”.

“This is a crisis made in Downing Street,” he said. “There are now 120,000 children homeless in temporary accommodation each night, but deep Conservative cuts to housing investment mean the number of new social rented homes has fallen to a record low.

“We can’t help those who are homeless if we don’t build the homes, which is why Philip Hammond must use the budget on Monday to back Labour’s plans to build a million genuinely affordable homes over the next 10 years.”

London’s deputy mayor for housing, James Murray, said Sadiq Khan, the mayor, was spending £1bn on new council homes in the capital, but that wwould not be enough to fix the housing crisis.

“Ministers must step up, by giving councils the money they need to help homeless people now, and by giving us the powers and resources we need to build far more council homes for Londoners,” he said.

The housing minister, Heather Wheeler, said: “Councils should try to place homeless households within their own area, and they must take into account healthcare needs, jobs and schooling when finding a suitable property. We are investing more than £1.2bn in tackling homelessness.”

The government stressed that it spends more than £23bn a year on housing benefit, more than any other OECD country as a proportion of GDP on housing support.