Fresh doubts over pollution around Heathrow emerged last night.

The government was reportedly warned a year ago that it was “exposed on Heathrow” because it had failed to deal properly with the issue.

Former prime minister David Cameron was told in a Downing Street memo that he did not “yet have an answer on air quality”.

The comments by former Downing Street advisor Camilla Cavendish will raise doubts about the government’s ability to push plans for a third runway through parliament.

Theresa May is expected to make a key ruling on airport expansion in the south-east next week, with Heathrow seen as the overwhelming favourite.

The memo, seen by The Guardian, raised concerns about the government’s air quality plan. It warned that the blueprint “overclaims and underwhelms” by failing to tackle the number of diesel cars.

The memo added: “It leaves us exposed on Heathrow where we don’t yet have an answer on air quality.”

Cameron failed to make a final ruling on airport expansion last year and commissioned two fresh studies into air quality and noise associated with aviation.

The Times reported last week that both reviews had subsequently failed to uncover any major problems with Heathrow’s bid, clearing the way for the new prime minister to give the hub the green light.

But May faces fresh criticism after announcing that MPs would not be able to vote on her runway decision for at least 12 months.

Sir John Armitt, a former member of the Airports Commission, which recommended a third runway at Heathrow last year, said: “It is another delay and I am not quite sure why it takes a year for that debate to take place because there has been a lot of consultation and MPs are well up to speed on this issue.”

May defended the timetable, insisting that there had been “no delay” over the plan.

Speaking in the Commons yesterday, she said time was needed to go through the “formal process”, including a full consultation with local residents, before a vote by MPs.

“This is a subject that has been debated, discussed, speculated on for 40 years,” she said. “This government will take a decision.”

London mayor Sadiq Khan, who backs a second runway at Gatwick, said: “The government’s decision to yet again delay deciding where to build a new runway will cause unnecessary uncertainty for British businesses already struggling with Brexit.”

Gatwick chief executive Stewart Wingate said: “This is a highly significant last minute intervention as it comes from the person who was in charge of policy in Downing Street until just a few weeks ago.

“She makes crystal clear that air quality will once again choke off airport expansion if Heathrow is chosen – and she is in a position to know.

“It is exactly what happened in 2009 and the government is in danger of making exactly the same mistake if it chooses Heathrow again.

“Heathrow cannot wish away its location nor will simply changing the modelling used to predict future air quality levels fix this problem.

“Unlike Heathrow, Gatwick has never breached legal air quality levels and can guarantee it will remain within these levels with construction and operation of a second runway.

“Britain needs certainty after decades of delay. This leaked memo shows that can only mean Gatwick.”