The ex-Tory cabinet minister has been questioned in relation to allegations by a woman she was sexually assaulted at the age of 19.
The Independent on Sunday says Lord Brittan, as he is now known, is understood to have been questioned last month about the claim, which relates to an incident in London in 1967.
Met Police are investigating claims that alleged incident took place at Lord Brittan’s London flat.
Downing Street last night refused to be drawn on whether David Cameron had been made aware of the extraordinary claims and added “we are not commenting.”
The former Tory, who married wife Diana in 1980, is understood to have strongly denied the allegations to police. Refusing to comment about the police probe, Lord Brittan reportedly said: “I’m sorry I’m not going to talk about anything like that.”
Lord Brittan was home aecretary in Margaret Thatcher’s Conservative government between 1983 and 1985.
At the time of the alleged incident Lord Brittan was not an MP after unsuccessfully contesting the North Kensington seat in 1966.
The police interview is said to have taken place at the central London offices of Mishcon de Reya.
In a statement about the rape allegations, the Met Police said last night: “In late 2012, a woman alleged to the Metropolitan Police Service that she was raped by a man in 1967 at an address in London.
“The woman was over the age of 18 at the time of the incident. The allegation is being investigated by officers from the Sexual Offences, Exploitation and Child Abuse Command.
“In June 2014, a man aged in his 70s was interviewed under caution by appointment at a central London location in connection with the allegation. He was not arrested. Enquiries continue.”