Campaigners have called for renewed action to tackle Britain’s housing crisis after official figures indicated a surge in rough sleeping in England’s cities, coupled with record number of families living in overcrowded homes.

Charities said welfare cuts, soaring rents and shortages of affordable homes were behind steep rises in street sleeping in London, Birmingham, and Manchester. There were 1,283 rough sleepers in the capital alone, a 13% increase, according to official figures

The data for England as a whole, based on estimates after a single night snapshot in the autumn, disclosed that 4,677 people bedded down on the streets or in sheds and tents in 2018. This is 165% higher than in 2010, and charities said the latest figures were likely to be an underestimate.

By illustration, separate rough sleeping figures for London alone released on Thursday by the CHAIN database and regarded as a more robust index of the scale of the problem, identified 3,289 rough sleepers in the capital between October and December, up 25% year on year.

“It’s a damning reflection of our society that night after night, so many people are forced to sleep rough on our streets – with numbers soaring in the capital – especially when we know that with the right commitment, rough sleeping could be ended for good,” said the chief executive of the Crisis charity, Jon Sparkes.

The 10 local authority areas with most rough sleepers were: Westminster, where a 41% annual rise took numbers to 306; Camden (141); Manchester (123); Birmingham (91); Bristol (82); Newham (79); Enfield (78); Hillingdon (70); City of London (67), and Brighton and Hove (64).

Meanwhile the English Housing Survey revealed that at least a million people in rented homes are now enduring overcrowding. Some 300,000 households in social housing were overcrowded – the highest since records began 25 years ago – while 250,000 in the private rented sector were squeezed into too few rooms.

The former Labour leader Ed Miliband, who is leading a campaign to build over 3m social homes in the next two decades, said the overcrowding figures were “more evidence of the human cost of the housing crisis which blights the lives of so many people”.

The rough sleeping figures came amid renewed concern about the risks of bedding down outside, especially as temperatures plummet. It emerged on Thursday that four homeless people in Oxford have died since November. The death on a Birmingham city centre street of rough sleeper Kane Walker was reported earlier this week.

Nearly 600 homeless people died on the streets or in temporary accommodation in England and Wales in 2017, up 24% in five years, according to official figures published in December. The average age of a rough sleeper at death was 44 years for men and 42 years for women.

The rough sleeper figures did show some improvement outside cities: across England there was a modest 2% fall – equivalent to 74 people, and the first time in eight years that national figures have not risen. Separate housing statistics showed that after more than a decade of decline, the proportion of 35-44-year-olds owning their own homes had increased.

The communities secretary, James Brokenshire, who launched the government’s rough sleeping strategy last year, said he needed to go further. “While these figures are undoubtedly a step in the right direction, I do not underestimate the task ahead in achieving our ambition of eliminating rough sleeping altogether by 2027.”

Around two-thirds of the 89 councils who received special government grant funding last year to hire outreach staff and create hostel beds also managed to reduce numbers of rough sleepers in their area, according to the official statistics, suggesting that concerted political and financial investment may pay dividends.

Rough sleeping figures fell overall in the south-east, the south-west, and east of England regions, the official figures show. Brighton and Hove saw the biggest fall, down 114% year on year, despite this it remains one of England’s homelessness hotspots.

However,John Healey, the shadow housing secretary, said the figures were desperately disappointing. “Ministers must do much more to make good the huge damage done over the last eight years. This new count shows that rough sleeping has more than doubled since 2010, but even these figures mask the true scale of the problem, as the government’s numbers are well known to be flawed and a massive undercount of the true level of rough sleeping.”

Rough sleeper figures are based on one-night counts or paper estimates carried out in October or November. It defines rough sleepers as people sleeping, about to bed down or bedded down on the street, in doorways, parks, tents and sheds but not hostels or shelters. Officials admit ensuring data accuracy through this approach is “inherently difficult”.

Polly Neate, chief executive of housing charity Shelter, said although the apparent stabilising of national rough sleeper figures was “rare piece of good news” it would have limited effects without wider measures to tackle social housing shortages, high rents and a failing social security benefits system.

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The Chartered Institute of Housing deputy chief executive, Gavin Smart, said: “To truly get to the root of the problem, the government must invest in more genuinely affordable housing as well as reviewing the impact of welfare reforms like the benefit cap, universal credit and the housing benefit freeze for private renters.”

Depaul UK homeless charity’s chief executive, Mike Thiedke, said: “Rough sleeping will not end unless issues with the benefits system are sorted out. Universal credit should be helping people to escape homelessness but, instead, it is trapping people on the streets, preventing them from finding a safe place to live.”