Sky News understands that the MP was accused by a young woman who worked in parliament.
He was arrested and taken to an east London police station on Saturday morning and released on bail Saturday evening.
A police statement said: “On Friday, July 31, the Metropolitan Police Department received allegations relating to four separate incidents involving allegations of sexual offenses and assault.
“These offenses were reportedly committed at addresses in Westminster, Lambeth and Hackney between July 2019 and January 2020.
“The Met has opened an investigation into these allegations.
“A man in his 50s was arrested on Saturday August 1 on suspicion of rape. ”
The story first appeared in The Sunday Times.
Sky News understands that the woman’s complaint was brought to the attention of a fellow MP, who raised it with Chief Whip Mark Spencer and with Jacob Rees-Mogg, the Leader of the House of Commons.
She then went to the police.
A statement from the Conservative Party said, “We take all allegations of this nature extremely seriously. As this matter is now in the hands of the police, it would be inappropriate to comment further. ”
A statement from Mr Spencer said: ‘The Chief Whip takes all allegations of harassment and abuse extremely seriously and has strongly encouraged anyone who has approached him to contact the appropriate authorities, including the Independent Complaints System and of complaints of Parliament, which can confidential inquiries. “