The economic boost from a Heathrow third runway could be a tiny fraction of previous estimates, government analysis shows, while the overall trade-off from the bigger airport could set the UK back by as much as £62.5bn.

As ministers promised to speed up expansion of the London airport in the name of economic growth, documents prepared by the Department for Transport said the runway was expected to boost GDP by only up to 0.05% – 90% less than the 0.5% previously stated.

The figures, described as historically bad by one economist, put the arguments for a third runway in fresh doubt. The DfT calculates the net present value of the scheme, even if entirely privately financed, to be between -£23.4bn and £-62.5bn. Net present value is defined by the DfT as the overall social value of expanding Heathrow, compared with not doing it, adding all costs and benefits.

That figure incorporates between £29bn-£42.4bn in positive benefits to passengers – primarily, lower air fares – and wider economic benefits.

But the government’s assessment is that those gains are outweighed by the social and environmental impact of building the runway. Profits at airlines and other airports are expected to fall by around £25bn, according to the appraisal.

The chancellor, Rachel Reeves, has championed rapid expansion of Heathrow in the name of economic growth, which she described as “this government’s top priority” as the consultation for the next stage of legislative was launched on Thursday.

The documents state that “external analysis, commissioned by the DfT, has found that the scheme could add up to 0.05% to GDP in 2056”.

Figures previously cited by the government have been in the range of 0.43%-0.5% growth.

Heathrow said the new figures did not capture all the economic benefits, while a government spokesperson said they were “only part of the picture”.

However, Alex Chapman, head of economic policy at the New Economics Foundation said: “In its desperation for a fraction of a percent of GDP growth, this government has lost its way. They said they were backing Heathrow expansion for economic reasons but their own analysis shows it won’t deliver.

“The results from the department’s impact assessment must be some of the worst in history, and reflect what we’ve been saying for the past year: the economic argument for expansion does not add up.”

A DfT spokesperson said: “Net present value is just one part of the overall picture – crucially, an expanded Heathrow could support over 60,000 new local jobs and deliver £40bn of benefits to the UK.

“This will attract international investment and strengthen Britain’s connectivity, and we have been clear that expansion will be financed by the private sector.”

Heathrow said the DfT appraisal model excluded other ways in which expansion could increase the UK’s economic competitiveness and did not capture the value of UK trade.

It said the Treasury had consistently found that a bigger airport would grow the economy and benefit the UK, and was backed by trade unions, regional airports and businesses.

The documents were published as the government announced the next stage in rapid approval of the third runway, with a consultation before a MPs vote, and ministers promising spades in the ground by 2029.

Heathrow’s proposed 3,500-metre runway would divert the M25 motorway and demolish about 800 homes, to add about 276,000 extra flights a year. The scheme is estimated to cost £33bn, although a recent independent assessment for the Civil Aviation Authority said the project was likely to cost between £32.7bn and £52.4bn.

A DfT health impact assessment separately showed that the third runway could significantly harm the health and wellbeing of up to 3 million people living near Heathrow. The official report said an expanded Heathrow was also likely to worsen access to housing, education, healthcare, open space, and transport, as well as affect water quality and community cohesion.

The Lib Dem transport spokesperson, Olly Glover, said: “Labour can’t show how a Heathrow expansion squares with our climate commitments, or that it can be delivered anywhere near legal noise and air pollution limits.”

“Real leadership delivers economic progress without trashing our climate commitments or steamrolling the communities in the flight path.”