Lord Brittan has said an historical allegation of rape against him is "wholly without foundation".
The former home secretary confirmed he had been questioned by police about a "serious allegation made against me".
The Independent on Sunday said Lord Brittan was understood to have been questioned last month about the claim, which relates to an incident in London in 1967.
Lord Brittan, 74, was not an MP at the time of the alleged rape.
In a statement, the Conservative peer said: "It is true that I have been questioned by the police about a serious allegation made against me. This allegation is wholly without foundation."
Scotland Yard said that in late 2012 a woman claimed to police that she was raped by a man at an address in the capital. It said the woman was over 18 at the time of the incident.
Police added that a man in his 70s was interviewed under caution, by appointment, at a central London location last month. He was not arrested and inquiries continue.
Lord Brittan was home secretary in Margaret Thatcher's Conservative government from 1983 to 1985.
Lord Brittan, who was first elected as an MP in 1974, later became Trade and Industry Secretary. He stood down from the Commons when he became a European commissioner in 1989.
Downing Street sources have said they did not know about the questioning.