The ex-minister, who has not been named, is alleged to have assaulted a woman and forced her to have sex – and the abuse allegedly took place during a relationship, The Sunday Times and Mail on Sunday reported.
The Metropolitan Police said it received allegations on Friday of sexual offences and assault relating to four separate incidents at addresses in London, including in Westminster, between July last year and January this year.
A spokesman for the Met said: “The Met has launched an investigation into the allegations.”
A man was arrested on Saturday on suspicion of rape and was taken into custody at an east London police station, the force added.
He has been released on bail to a date in mid-August.
The papers said the allegations were raised with Tory Chief Whip Mark Spencer, and the complainant also spoke to him – but no action was taken.
The PA news agency understands Mr Spencer advised her to make a formal complaint to the authorities who would be able to investigate the claims.
A spokesman for Mr Spencer said: “The Chief Whip takes all allegations of harassment and abuse extremely seriously and has strongly encouraged anybody who has approached him to contact the appropriate authorities, including Parliament’s Independent Complaints and Grievance Scheme, which can formally carry out independent and confidential investigations.”
A Conservative Party spokesman 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.”
The investigation comes days after former Conservative MP Charlie Elphicke was convicted at Southwark Crown Court in a separate case of sexually assaulting two women, one of whom was a parliamentary worker.
