Targets for new homes are likely to be missed by half of England’s local authorities, according to a damning assessment of the government’s housing strategy, while increasingly profitable building companies are getting away with paying less for infrastructure and more than half of councils have failed to draw up adequate plans to solve the housing crisis.

The National Audit Office (NAO) concludes that the planning system in England is “not working well” and says councils are struggling to negotiate successfully with developers, leaving swaths of the country vulnerable to either housing shortages or situations where the wrong homes are built in the wrong places. Since 2010 there has been an almost 40% real-terms cut in spending on planners, according to the public spending watchdog.

The NAO report follows claims from Conservative ministers that housebuilding is a top policy priority and that by the mid-2020s the rate will increase to 300,000 new homes a year. Between 2005-06 and 2017-18 the housebuilding rate has averaged 177,000 a year and the annual number has never exceeded 224,000.

Separately, a study by the National Housing Federation (NHF) has found that an estimated 1.3 million children are living in poverty in privately rented homes in England, an increase of 69% since 2008. Its report says 242,753 of these children would not be living in poverty if they had access to social housing as their parents would be paying lower rents.

Kate Henderson, the NHF’s chief executive, said: “It is a disgrace that in one of the wealthiest countries in the world we cannot provide our children with a secure and affordable home. The critical lack of social housing is pushing more and more families into poverty by forcing them into insecure privately rented homes they cannot afford.”

The NAO report cites research by a planning and development consultancy, Lichfields, which found that in 2020 about 50% of local authorities are likely to fail the test for building enough homes and could face penalties, including giving developers in those areas greater freedoms regarding where they can build.

The report says only 44.1% of local authorities had up-to-date plans setting out how they could meet the need for new homes.

Government figures show that while the average contributions agreed with developers for public infrastructure such as schools, health centres, roads and social housing remained at about £19,000 per new home between 2012 and 2017, average house prices increased by 31% in that period. The top five developers’ average operating profit margin increased from about 12% to 21%.

Only 47% of local authorities had implemented a community infrastructure levy, intended to raise money from developers. The Ministry of Housing, Communities and Local Government told the NAO that town halls may not have the commercial and negotiating skills needed to deal with developers’ arguments on viability and that some were unable to negotiate effectively.

The report also found that planning appeals were taking longer and between 2010-11 and 2017-18 there was a 37.9% real-terms fall in net expenditure on planning functions.

Kit Malthouse, the housing minister, said he recognised the challenges identified by the NAO. “Over the last three decades, governments of all stripes have built too few homes of all types,” he said, adding that the figure of 220,000 homes built in 2017-18 was higher than in all but one of the last 31 years.

“We’re conducting independent reviews on build-out rates and planning inquiries,” he said. “And through multibillion-pound funding, planning reforms and giving councils the freedom to borrow more to build homes, we’re helping to make the housing market work for everyone.”