Lawyers for the family of a Brazilian man shot dead by police have called on the Independent Police Complaints Commission to speed up its inquiry.
The leak suggests the electrician was restrained before shot
After talks with the IPCC, solicitor Gareth Peirce said a further public inquiry was needed to sort out the "chaotic mess".
The family of Jean Charles de Menezes, 27 - mistaken for a suspected suicide bomber - wanted answers, she added.
The IPCC is to issue a statement but said the talks had been "constructive".
Investigation papers, leaked to ITV News, suggest the Brazilian electrician was restrained by a surveillance officer before being shot eight times on 22 July - a day after the failed London bombings.
The documents contradict initial eyewitness reports suggesting Mr de Menezes had hurdled a barrier at Stockwell Tube station and was wearing a padded jacket.
Ms Peirce said: "The situation demands something fast for public interest as well as the family's interest.
"There have been lies that have been told and there have been lies that have been allowed to remain uncorrected."
She also said: "A public inquiry is, in fact, the only kind of inquiry that can deal effectively with the big policy issues brought up in this case, whether or not there is a prosecution or inquest."
On the day of the shooting, Scotland Yard said that "his clothing and his behaviour at the station added to [the officers'] suspicions".
But the documents suggest Mr de Menezes was wearing a denim jacket and walked into the station, picked up a free newspaper, walked through ticket barriers and only started to run when he saw a train arriving.
Jenny Jones, a member of the Metropolitan Police Authority, told the BBC she had faith in what the IPCC was doing, but said she also wanted a public inquiry into what happened.
"The fact that there's been a leak has to demonstrate that there are problems with the procedure, and I therefore think it's time now to come clean and actually let us all know exactly what's been going on," she said.
Ms Jones also called for "the guidelines the police are using for this shoot-to-kill policy" to be made public.
"The guidelines are clearly confused if people can make a mistake.
"The best way of mopping up any confusion is to make sure that there is some sort of democratic oversight, so we have to see those guidelines."
The BBC's home affairs correspondent Daniel Sandford says there was also a "growing focus" on Metropolitan Police chief Cressida Dick, reportedly in charge of the firearms unit when the shooting happened, and reports there were "confused commands" about the shoot-to-kill policy coming from her.
The Daily Mirror newspaper said she told the surveillance team Mr de Menezes should be detained before he reached Stockwell Tube station.
But ITV News said the 44-year-old also told officers: "Whatever you do, do not let him get on the Tube."
Labour MP Ann Cryer, who sits on the Commons Home Affairs Committee, is calling for a review of the shoot-to-kill policy.
An image leaked to ITV shows Mr de Menezes lying dead on the Tube
She told BBC News: "We normally go through the procedures of apprehension, prosecution, conviction and punishment.
"If you have a shoot-to-kill policy, where does all that go?"
But London Mayor Ken Livingstone said the bombings had presented the Metropolitan Police with their "most difficult challenge" and the approach taken by its commissioner, Sir Ian Blair, was the only way to defeat terrorism.
"The speculation and leaks taking place in the media are not the best way to deal with such a serious matter as the shooting at Stockwell Tube station," Mr Livingstone added.
"Everyone involved in this terrible tragedy is entitled to get their information from the IPCC at the proper time in the proper way, not through selective leaks and media speculation."
The brother and cousins of Mr de Menezes were due to travel from Brazil to the UK in the next few days, said another family lawyer, Harriet Wistrich.
She added that attempts were also being made to fly the victim's parents to Britain.