Heathrow is edging closer to securing government approval for a third runway after the airport indicated that a last-minute Whitehall study into concerns over pollution will give the all-clear.

The airport’s chief executive, John Holland-Kaye, said he had “no reason to believe” that any issues had been raised in research conducted this year by the Department for Transport into air quality around Heathrow, despite consistent breaches of legal limits. He said: “Everything we have seen suggests that it won’t be an issue. I suspect if it were we would know about that by now.”

The comments came as it emerged that a cabinet subcommittee on Heathrow will not make a final decision on Tuesday, as previously thought, but on 25 October. Theresa May’s spokeswoman refused to comment on reports that the full cabinet would discuss the matter on Tuesday, stressing that she would not disclose in advance the content of cabinet meetings.

Holland-Kaye told the Guardian that a recent independent study by Cambridge researchers into air quality, separate to the DfT study, had bolstered Heathrow’s case. He added that pollution studies had not taken into account further mitigation measures put in place by Heathrow that would counter the pollution impact from car traffic created by millions more passengers using an expanded airport.

The Heathrow boss also claimed that approving a third runway was no longer the difficult political choice for the prime minister. “What was once seen as a difficult political decision is becoming a much easier one.”

He pointed to support for expansion demonstrated on Monday in letters to May from 50 MPs and representatives from the major parties in the Scottish, Welsh and Northern Irish devolved assemblies, as well as from representatives of Britain’s largest union, Unite. Labour sources also said the party would back a third runway, despite the opposition of the leader, Jeremy Corbyn, and the shadow chancellor, John McDonnell. The shadow transport secretary, Andy McDonald, said the “imperative was overwhelming” for more capacity and implied he would back Heathrow over Gatwick.

With 25 October looking the most likely date for the government to finally respond to the Airports Commission report of July 2015 that recommended expanding Heathrow, May’s spokeswoman denied that the decision had been pushed back – saying that the decision would come “soon”. Ministers have never ruled out the rival plans of Gatwick, which hopes to build a second runway, while a third option, to lengthen one of Heathrow’s existing runways, remains on the table.

“The government is very clear on the importance of making a decision, the need that there is to address the problems around airport capacity and the huge potential economic opportunities of airport expansion,” said the spokeswoman.

“Clearly it’s a decision that it’s important to get right so that future generations can benefit.” She added: “You can expect the decision soon. There has been no change in timing.”

The cabinet subcommittee deciding will exclude prominent ministerial opponents of Heathrow, such as Justine Greening and Boris Johnson. Heathrow remains confident that most MPs will back its plans.

Holland-Kaye said: “The benefit of the Airport Commission process is that it’s got us to a place where we’ve got a much better plan. It’s been a public process where we’ve consulted with communities on what’s acceptable.”

He said that by meeting new conditions and altering the scheme, the airport’s expansion now had the backing “of business, politicians, and unions, and even support from local people”.

As a result, Holland-Kaye said: “It makes it far more deliverable. It’s got far more support than other infrastructure projects such as HS2.”

While he said the imminent decision was the key moment, he promised that Heathrow would “keep on listening” to communities while drawing up plans.

The third runway could be built by 2025 and would cost £17.6bn.

Gatwick airport has also said it will remain on standby to deliver its own plan for a second runway even if Heathrow’s gets the green light next week. London’s second airport believes that legal and political challenges will halt the west London hub’s expansion once again.

It warned again on Monday that the number of people overflown by a new runway at Heathrow would be 70 times more than would be affected by a second runway at Gatwick. A new runway at Heathrow would affect 278,000 people compared with 3,800 for Gatwick’s plans. New flightpaths at Heathrow would cross prime residential areas of London whose inhabitants have so far escaped aircraft noise, including St John’s Wood, Maida Vale, Kensington, Notting Hill and Shepherd’s Bush.

Gatwick’s chief executive, Stewart Wingate, said: “The difference in noise impact between the two schemes is stark. We have to decide whether to ignore the views of a million Londoners whose health will be affected by constant noise, or expand Gatwick, the environmentally responsible option where we can cap the number most affected by noise.”

Meanwhile, Greenpeace said it had joined forces with councils surrounding Heathrow to launch a legal challenge to any new runway. The environmental campaign group said it would contribute costs alongside Hillingdon, Richmond, Wandsworth and Windsor and Maidenhead councils to instruct lawyers to seek a judicial review over the environmental impacts of a decision to go ahead.

The Greenpeace UK executive director, John Sauven, said: “A third runway at Heathrow would be an air pollution and carbon timebomb.”