Leon Brittan's brother has said Labour deputy leader Tom Watson should apologise after police dropped a rape inquiry against the former home secretary.
Sir Samuel Brittan accused the MP of making "unfounded accusations" which had prompted police to reopen the case against Lord Brittan.
It comes after the Times reported that Scotland Yard deputy assistant commissioner Steve Rodhouse had written to Lord Brittan's widow to apologise for failing to tell the family the peer had been cleared before his death.
Lord Brittan died of cancer earlier this year and was unaware that police had decided there was no case for him to answer over allegations that he raped a 19-year-old student in 1967.
Journalist Sir Samuel told the Daily Mail: "He should apologise to my sister-in-law for making unfounded accusations against my brother. And he should apologise in public as well."
The Crown Prosecution Service found in July 2013 that there was not enough evidence for a prosecution, but the decision was never passed on to the peer.
The case was reopened last year after Watson wrote to the Director of Public Prosecutions and Lord Brittan was interviewed under caution, when he was seriously ill.
Former Conservative chancellor Norman Lamont, a friend of Lord Brittan, said police investigations of historical sex abuse risked becoming a "witch-hunt".
Writing in the Daily Telegraph, he said: "I visited Lord Brittan several times in his last days and saw the suffering of a man under the shadow of the vilest accusations. This was an extremely painful time for his wife.
"After his death came the police raid on his two houses, while his widow was still sorting out his belongings, some of which were carted away. As with Cliff Richard, the police were accompanied by press and television.
"Before Lord Brittan died, the police, referring to a rape accusation, suggested he should take part in an identity parade. That seems beyond satire. How could a well-known public person, already named and identified by his accuser, usefully take part in such a charade?"
The case had been "mishandled at every level", Lord Lamont added.