Scotland Yard "initially resisted" the investigation into the shooting of Jean Charles de Menezes, the Independent Police Complaints Commission has said.
Mr Menezes was shot a day after the failed London bombings
The inquiry was not formally handed over to the IPCC until five days after the Brazilian was shot dead by police at Stockwell Tube station on 22 July.
Lawyers for Mr Menezes' family said vital evidence could have been lost.
Denying a cover-up and calls to resign, Met chief Sir Ian Blair said: "My job is to stay here looking after London."
Sources said a member of the IPCC secretarial staff had been suspended during an investigation into the source of the leaked papers.
Mr Menezes was shot after police mistook him for a suicide bomber. The shooting came a day after the failed 21 July attacks on the London underground and a bus.
The BBC has also learned the shooting was not captured on Stockwell Tube's CCTV because police officers had removed the cameras' disks for their investigation into the suicide bomb suspects who boarded the train at the same station the previous day.
A lawyer for the Menezes family, Gareth Peirce, is calling for a public inquiry into the case to sort out the "chaotic mess".
Friday: IPCC called in
Monday: IPCC takes over the case from the Met
Wednesday: Formal legal handover completed
There are concerns the delay in beginning the investigation could hamper it
But Scotland Yard chief Sir Ian Blair says he was at the handover on Monday, and did not know why the probe was delayed until Wednesday
After meeting the IPCC she said: "We expressed our extreme concern that although they [the IPCC] have a statutory duty to investigate from the very moment of a fatal death at the hands of the state, they were not there."
Metropolitan Police Commissioner Sir Ian Blair wrote to the Home Office on the morning of Mr Menezes' death to make sure the terrorist investigation took precedence over any IPCC probe.
On Thursday, Sir Ian told BBC Radio Four's Talking Politics he would not have written the letter had he wanted to "cover something up".
"At that stage I and my officers thought the dead man was a suicide bomber and we were in the middle of the biggest counter-terrorist operation," he said.
He said he had written to ask the Home Office if it would be "wise to bring another set of investigators into the middle of that".
An image leaked to ITV shows Mr de Menezes lying dead on the Tube
"Secondly, the IPCC has a duty - which I respect - to inform the family of everything they find and this is an investigation that involves secret intelligence," he added.
The investigation had been handed over to the IPCC "after we had considered those points" on the Monday after the shooting, as was appropriate in the "unique situation".
Sir Ian told the programme he knew nothing about allegations the IPCC inquiry had been delayed for a further two days.
On the day of the shooting, a Scotland Yard spokesman had said that Mr Menezes' "clothing and his behaviour at the station added to [the officers'] suspicions".
But investigation papers, leaked to ITV News, suggest the Brazilian electrician was wearing a denim jacket and walked into the station, picked up a free newspaper, walked through ticket barriers and started to run only when he saw a train arriving.
The documents contradict initial eyewitness reports suggesting Mr Menezes had hurdled a barrier at Stockwell Tube station and was wearing a padded jacket.
But Sir Ian told Talking Politics those reports had never been confirmed by Metropolitan Police officers, who "do not spin".
Mr Menezes' "tragic" death had to be seen in the context of what was "the largest criminal inquiry in English history", Sir Ian told the programme. "It is one death out of 57."
The IPCC refused to comment on claims that a member of staff had been suspended over the leak.
But it said in a statement: "Both the IPCC and the Metropolitan Police Service recognise that the unauthorised disclosure of information cannot be ignored and must be addressed."
Its focus was on the "search for the truth", it added.
Earlier, the commission's deputy chairman John Wadham said Scotland Yard had "initially resisted us taking on the investigation - but we overcame that. It was an important victory for our independence."
Mr Wadham said the IPCC was looking forward to meeting Mr Menezes' family and that he was confident he would be able to answer all their questions.
The inquiry was "making good progress" and should be completed within three to six months, Mr Wadham said.
The BBC's interview with Sir Ian Blair will be broadcast in full on Radio 4's Talking Politics programme at 1100 BST on Saturday, 20 August.