They handed it into cabin crew after finding it on a plane flying from New York to Heathrow yesterday.
One of the former prime minister’s bodyguards is thought to have removed his weapons holster to use the toilet and forgotten to pick it up again.
As the pilot knew armed officers were travelling with Mr Cameron, he decided to continue with the flight.
A Metropolitan Police spokesman said: ‘We are aware of the incident on a flight into the UK on 3 February and the officer involved has since been removed from operational duties.
‘We are taking this matter extremely seriously and an internal investigation is taking place.’
The gun is believed to have been a 9mm Glock 17 pistol, the Daily Mail report.
A source told the paper: ‘Fortunately it was found by a law-abiding member of the public who did the right thing.
‘If it had been found by someone with malign intent it could have turned into a very serious incident for everyone on board.’
As a former prime minister, Mr Cameron is entitled to round-the-clock armed protection for life from Scotland Yard’s Specialist Protection Branch, which is taxpayer funded.
One of the passengers, a 33-year-old businessman told The Sun: ‘There was a real commotion going on with a guy near to me. He said he had found a gun in the toilets, which was met with disbelief.
‘A few minutes later the captain came into our section and confirmed a gun had been found – which freaked everyone out.
‘He tried to calm everyone down by explaining that the law allowed handguns on planes for protection officers and that the gun was back with the bodyguard.’
Another passenger told the paper: ‘We were waiting to take off when a guy started to show pictures on his phone of a gun and two passports – one was David Cameron’s – he said he found in the toilet.
‘They were just resting on the side by the sink. He was stunned by what he saw.’
Mr Cameron is thought to have been in New York for the weekend with his wife Samantha.