The true cost of Heathrow airport expansion to the taxpayer is not being divulged by the government, according to a Conservative former transport minister, who said ministers needed to “come clean” over the probable £5bn-£10bn public cost for road and rail links.

Tory MP Stephen Hammond raised his concerns as it emerged that Heathrow executives would get millions in bonuses for securing approval for the £17.6bn third runway scheme.

Hammond, a transport minister from 2012-14 when the airports commission was studying the scheme, said the government was misinforming the public by announcing that: “Expansion costs will be paid for by the private sector, not by the taxpayer.” The transport secretary, Chris Grayling, had also omitted this in his statement to the house, he said.

Facebook Twitter Pinterest MP Stephen Hammond says Heathrow expansion costs will not fall to the private sector as ministers claim. Photograph: Julian Makey/Rex Features

“There will be a number of specific things we will be doing for Heathrow. The government and Heathrow need to come clean on what the cost to the taxpayer is going to be. No one would be surprised if it is £5bn, but we should just be honest about it,” Hammond added.

While the commission report estimated a £5bn bill for new roads and rail links, Transport for London put the potential cost as being as high as £18.4bn.

Heathrow said it had earmarked just £1bn, and that it only accepted direct responsibility for works to the M25, which the third runway would cross, and a few minor roads. The airport contends that it will be cutting traffic, despite adding up to 55 million passengers a year, and that revenues could offset the bill.

Heathrow confirmed on Wednesday that executives would be paid bonuses, for securing a new runway, that would be expected to run into several million pounds. A spokeswoman said the bonuses would depend on also reaching targets on customer service and profitability.

The bonus scheme, devised by Heathrow’s chief executive, John Holland-Kaye, and approved by shareholders last year, will mean senior managers getting rewards based on net earnings, passenger service and strategic targets for a third runway .

Holland-Kaye earned £2.06m last year including bonuses, more than doubling his basic salary of £885,000. The new scheme, linked to expansion, did not pay out in 2015, “as the performance in respect of this scheme is so uncertain at this stage”, according to the airport’s annual report.

In an unusual move, a further payment will depend on employee satisfaction and engagement scores, known as the “mojo bonus”, after “internal motivational practice” that was developed by Holland-Kaye.

Facebook Twitter Pinterest Nelson’s statue in central London wears a mask after Greenpeace action this April highlighting air pollution. Photograph: Matt Dunham/AP

Mojo may be rising at the airport faster than in the surrounding boroughs, where concerns over noise and air pollution have been heightened by a Department for Transport report into air quality. Campaigners have highlighted an apparent admission that pollution is likely to rise in parts of London with a third runway, which they say potentially makes the scheme illegal.

The report, produced by Parsons Brinckerhoff for the DfT, said that Heathrow was “at risk of worsening exceedances of limit values alongside some roads within greater London, but this would be unlikely to affect the overall zone compliance”.

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However, this is likely to be contested. Legal opinion obtained by the Clean Air in London campaign, from Robert McCracken QC, states that worsening pollution in any areas that already exceed legal limits would break the law.

Grayling has said that the runway cannot go ahead without complying with air quality obligations, which the report suggests would be entirely dependent on proposed mitigation schemes from Heathrow.

A DfT spokesperson said: “The government believes that the Heathrow north-west runway scheme could be delivered without impacting on the UK’s compliance with air quality limit values, with a suitable package of policy and mitigation measures.“

Jenny Bates, Friends of the Earth pollution campaigner, said: “With 10,000 early deaths in the capital each year from air pollution this approach shows a callous disregard for people’s health. We believe this approach is at odds with EU rules on tackling air pollution.”

In the Commons, the prime minister, Theresa May, said the government had “looked very carefully at the air quality issues”. Challenged by Tanya Mathias, the Tory MP for Twickenham, on worsening air pollution and noise, May said: “The evidence shows that air quality requirements can be met.”

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Earlier, Grayling endorsed the idea of building the third airport runway over the M25 using a bridge rather than digging a tunnel for Britain’s busiest motorway to pass underneath the runway. He said the scheme would minimise disruption to motorists and be cheaper than the tunnel, which has alarmed Highways England, the strategic roads authority.

While the so-called “ramp” has raised eyebrows, engineers insisted it was standard global practice. Chris Chalk, of the Institute of Civil Engineers transport expert panel, said: “Clearly there will have to be all sorts of simulations to ensure there is no risk of distracting drivers.” He said there would be a 150-metre width of bridge each side of the runway and that the gradient would be less steep than that on the runways at Manchester and Birmingham airports.