Lord Brittan, as he is now known, was understood to have been interviewed at the office of his lawyers under caution last month after a woman claimed she was raped in London in 1967 when she was 19.
The Conservative peer is thought to strongly deny the allegation and was quoted as saying, “I’m sorry, I’m not going to talk about anything like that”.
Downing Street last night refused to be drawn on whether Prime Minister David Cameron had been made aware of the claims against Lord Brittan, who was made a life peer in 2000.
Asked about the allegations, a No10 spokeswoman said: “We are not commenting”.
Former Tory minister Lord Brittan, who married in 1980, is understood to have strongly denied the allegations to police.
A Met Police spokesman said: “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. Inquiries continue.”
The allegation against Lord Brittan is not connected to separate claims involving a dossier compiled by an MP detailing allegations of a 1980s Westminster paedophile ring that was given to Lord Brittan when he was home secretary.
At the time of the alleged incident Lord Brittan was not an MP after unsuccessfully contesting the North Kensington seat in the 1966 general election.
He was elected as an MP in 1974 and was made Queen’s Counsel in 1978.
Between 1979 and 1981, he was minister of state at the Home Office and was then promoted to become chief secretary to the Treasury, becoming the youngest member of the Cabinet.
He went on to serve as home secretary in Margaret Thatcher’s government from 1983 to 1985.
In 1984, after the murder of British police officer Yvonne Fletcher during a protest outside the Libyan embassy in London, Lord Brittan headed the government’s crisis committee as both Mrs Thatcher and the foreign secretary, Sir Geoffrey Howe, were both away at the time.
In January 2014, secret government documents released by the National Archives disclosed that British officials were twice warned by Libya that the Libyan embassy protest would become violent – hours before PC Fletcher was killed.
Neither Lord Brittan or his lawyers, Mischon De Reya, commented on the issue when approached for a response yesterday.