Lord Brittan died before being cleared of rape after police sought a review of the case because a decision not to bring charges would attract media criticism and "public cynicism", it has emerged.
Scotland Yard repeatedly appealed for the Crown Prosecution Service to examine the evidence even though it had concluded there was "not a strong case" against the late politician.
The disclosures came as the force published a summary of findings from a report ordered after it apologised to Lady Brittan over the matter, which was also at the centre of controversy surrounding allegations raised by Labour deputy leader Tom Watson.
The Metropolitan Police admitted Lord Brittan's legal team should have been told no charges would have been brought if he was still alive at the same time as the complainant, who was informed in April.
In a lengthy statement the force also disclosed that commissioner Sir Bernard Hogan-Howe has asked a separate force to review the investigation to ensure it was thorough and properly conducted.
The case was sparked when a woman known as "Jane" made an allegation in November 2012 that she was raped in London in 1967, when aged 19.
Despite two separate inquiries determining that Lord Brittan should not face any action over the claims, he died in January unaware the case would not be pursued.
An investigating officer decided no further action should be taken and informed the complainant in September 2013.
However, a review was ordered in April last year and the following month Lord Brittan was interviewed under caution at his solicitors' office while suffering from terminal cancer. He denied the offence, stating he did not believe he had ever met the complainant.
The Met said that contrary to reports, the politician was not asked to participate in an identification parade, but a procedure was carried out in October involving the complainant being shown a series of images of men matching Lord Brittan's "broad appearance" in 1967.
In November officers submitted a file to prosecutors requesting "a transparent, external assessment of the case as a matter of public interest".
However, the CPS replied declining to consider the file because it "did not meet the appropriate criteria". Its guidelines state that cases should only be referred at this point if police believe there is sufficient evidence to charge a suspect.
Deputy Assistant Commissioner Steve Rodhouse, who had taken over as the Gold Commander for the investigation in July, decided to appeal against this decision.
The Met's statement said: "It was felt that these were highly unusual circumstances where the previous independence of the police to tackle sexual offending by VIPs had been publicly called into question.
"A decision to take no further action in respect of this allegation would undoubtedly have resulted in media criticism and public cynicism, and there was clearly a very strong public interest in ensuring that the correct decision had been made."
The Met said that Lord Brittan could not therefore have been told then that no action was being taken because, "although the MPS had concluded that there was not a strong case against Lord Brittan, the purpose of requesting a CPS view was to assess whether, in its view, it did reach the evidential standard".
The statement revealed that officers made a string of requests for the CPS to review the evidence both before and after Lord Brittan's death, which were finally turned down in June.
However, the force confirmed that the complainant had already been told in April that there would not have been a prosecution had Lord Brittan been alive.
A spokesman confirmed the full report, which has not been published, acknowledges that this was "premature" given the CPS's confirmation would not be received for two months.
Meanwhile, no contact was made with Lord Brittan's solicitors after they were made aware that a file was to be sent to the prosecutors following the identification procedure.
The Met admitted the former Home Secretary's legal team should have been informed at the same time as the complainant, saying this would have allowed them to clarify the position with his widow.
Relatives of those who die while under investigation are not normally informed what the outcome would have been, the force said, but conceded that "the public interest in the case required a different approach".
Scotland Yard said it was "important to recall" that the events took place against a backdrop of reports of allegations that it had failed to investigate allegations against politicians properly in the past.
In an apparent reference to Mr Watson, the Met said it accepts MPs' contact with police is "part of their Parliamentary duties", adding: "But the principle that police officers are independent when making decisions about operational matters is one that we firmly adhere to."
The Met revealed that the salary costs of officers involved in the investigation were almost £4,000 - not including the senior ranks and lawyers who scrutinised the process or the review.
In a letter to Home Affairs Select Committee chairman Keith Vaz, Mr Rodhouse responded to a series of questions about the investigation - including how much it cost taxpayers.
He said: "This investigation was conducted by officers engaged in a number of other investigations and was not separately costed. A brief assessment of the case indicates that the salary costs for the police officers who carried out the investigation are in the region of £3,800.
"This includes planning and conducting the investigation, preparing and submitting the files to the CPS. It does not include costs of supervision and governance through the Gold Group meetings through which senior officers and legal advisors scrutinise the investigative process. Nor does it include the costs of reviewing the investigation, legal support in drafting letters and communication support in dealing with enquiries from the media."
Mr Vaz said his committee would be expecting further answers from the Met in an evidence session on Wednesday, when Mr Watson is also expected to appear before the MPs.
"I am grateful to the Metropolitan Police for their prompt response, which raises further issues on which the committee will question them next Wednesday," he said.