Lord Brittan died in January 2015 without being told by police he would not face any action over a rape claim.
20:03, UK, Tuesday 16 February 2016
Scotland Yard chief Sir Bernard Hogan-Howe has apologised to Lord Brittan's widow over the handling of a historical rape allegation against her late husband.
The Brittan family said she accepted the "full apology" at the private meeting.
In a statement they added: "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.
Sir Bernard told BBC Radio London: "We had a private conversation. It was a constructive one and 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.
"Of course, as I say, it's a private conversation, I can't say an awful lot else. I thought it was important to meet her."
The former home secretary died in January 2015 without being told he would not face any action over the claim.
Police apologised to Lady Brittan in October, saying she should have been told in April that there would not have been a prosecution had her husband been alive.
Lord Brittan, a former home secretary, has also been named in connection with the controversial Operation Midland, a separate investigation into allegations of a VIP paedophile gang.
Sir Bernard said Operation Midland "has not yet been concluded".
He added: "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."