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 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, 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 Mr 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.

Tory MP Nigel Evans, who was cleared last year of a series of sexual abuse charges in a high-profile court case, said Lord Brittan's family now deserved an apology from the Labour deputy leader.

The former Commons deputy speaker said Mr Watson had "set himself up as judge and jury".

"It is really difficult to over-estimate the trauma that that family will have been pushed through," Mr Evans told the BBC Radio 4 Today programme.

"Even when Leon had died, Tom Watson decided to repeat the allegations. It is totally unfounded.

"As vocal as he was at that time, it is amazing that we have heard nothing from him since the revelation that the allegations were not going to be proceeded with."

Asked if Mr Watson should apologise, Home Secretary Theresa May did not give a direct answer, but said: "I think those of us in public life need to be very careful about the language we use and how we talk about things."

She also called for police to inform those who they decide not to proceed against of their decision as quickly as possible.

Mrs May said: "If there are specific allegations the people need to look into those and follow them up properly.

"And of course if they are not going to act against somebody then let them know as soon as is possible and practical to do so."

Appearing at the Women in the World conference in London, Mrs May said it was "absolutely right" that the independent child abuse inquiry was established.

She said: "It is looking at the lessons we need to learn, particularly about institutions which in very many cases had a duty of care to children and which failed in that duty of care."