The anti-noise body 2M, formed by councils in west London and adjacent counties, said the study believed to have cost£1m was published only after it applied pressure on the Department for Transport.
The councils said the survey indicates noise becomes a significant annoyance at 50dB compared to the 57dB restriction now in force.
The government is to decide shortly whether a third runway should be built at Heathrow. The study had been expected to help ministers make a decision.
But aviation minister Jim Fitzpatrick said that it had found “no identifiable threshold at which noise becomes a serious problem” nor a reliable way of attaching a financial value to its impact.
A review had recommended that the study should not be used to develop government policy, he said.
Wandsworth LBC leader Edward Lister (Con), called on the NAO to probe how much was spent “producing a report which the government now says cannot be used to help determine whether Heathrow should be allowed to get bigger”.
He added: “They did not want it published in advance of the third runway announcement. It was only the pressure from local councils that forced their hand.”