Lord Brittan's widow has accepted a "full apology" from Scotland Yard chief Sir Bernard Hogan-Howe over his force's handling of a rape allegation against her husband.
Lady Brittan had a private meeting with the Metropolitan Police Commissioner in London on Tuesday.
Britain's largest police force came under fire over its investigation into a claim that Lord Brittan raped a 19-year-old woman known as "Jane" in 1967 - which he denied.
In a statement, the family of the late politician said: "At the start of the meeting Sir Bernard offered Lady Brittan a full apology on behalf of the force, which she accepted.
"Lady Brittan went on to ask and table some 30 questions regarding the two police enquiries as they related to Lord Brittan.
"Sir Bernard promised to answer them in writing and Lady Brittan and the family await his response."
Lord Brittan died aged 75 in January last year without being told he would not face any action over the rape allegation.
Police originally determined that the complaint should not be pursued more than a year before his death. But the investigation was reopened and he was interviewed under caution in May 2014 while suffering from terminal cancer
Sir Bernard told BBC Radio London his conversation with Lady Brittan was "constructive".
He said: "I hope she found it helpful. I confirmed the apology that we made some months ago now.
"It is an apology for not telling her at an early stage about the fact that Lord Brittan, who by that stage unfortunately had died, was not to be prosecuted in the future.
"There was no chance of successful prosecution. She's had quite a few questions.
"I thought it was important to meet her. We had actually arranged it for a while ago but for various reasons it couldn't happen, but it did today."
Asked if Lady Brittan was accepting of the apology, Sir Bernard replied: "To be fair, I think you'll have to ask her. I don't think it's fair for me to try and answer for her, but certainly she didn't reject it."
Police first apologised to Lady Brittan in October, saying she should have been informed earlier that there would not have been a prosecution had her husband been alive.
Lord Brittan has also been named in connection with the hugely controversial Operation Midland, a separate inquiry into allegations of a VIP paedophile gang.
Sir Bernard said the investigation "has not yet been concluded".
He said: "As soon as it is, obviously we will announce whatever the outcome is.
"These things are never straightforward. They are historical investigations, which are quite hard to investigate.
"We've had suspects named - we don't do that - it's caused difficulty for investigators. And then during the investigation people say: 'Why don't you complete these things quicker?'
"Well one of the difficulties being that new witnesses come forward during the investigation. We've had to explore what they've said.
"There's been quite a lot going off in the background, but we don't share what happens in the investigation in the public domain."
A furore erupted over the investigation after D-Day veteran Lord Bramall was cleared.
His home had been raided and he was interviewed under caution before he was told in January he would face no further action.
There have been suggestions that the inquiry, which had cost £1.8 million as of November, is on the brink of collapse amid questions about the reliability of the central witness in the investigation, a man known as "Nick".
Former Tory MP Harvey Proctor, who furiously denied any involvement, has been interviewed under caution twice but there are unconfirmed reports that he will also be formally told he will face no further action.
The late former prime minister Edward Heath has also been named in connection with the inquiry.