Blunt, the MP for Reigate, has had the Conservative Party whip suspended and has been asked to stay away from parliament.
He is the latest in a line of Tory MPs to lose the party whip following allegations about their behaviour.
Asked about the problem, Keegan told Times Radio on Friday morning: “I certainly don’t see a cultural issue amongst Conservative MPs. I see individual incidents which are all investigated as such.”
“The prime minister’s been clear about high standards. He expects high standards and he always follows due process.
She added: “But, you know, all you can do with these things is deal with them as they arise and take the appropriate action.”
Surrey Police yesterday said a man was arrested on Wednesday before being released on conditional bail.
Soon after the reporting, Blunt published a statement on X, formerly known as Twitter, confirming he had been arrested.
He said the arrest was “unnecessary” and he is “confident” investigation will end without charge.
The statement said: “It has been reported that an MP was arrested yesterday in connection with an allegation of rape.
“I am confirming that MP was me. The fact of the arrest requires a formal notification of the speaker and then my chief whip.
“I have now been interviewed twice in connection with this incident, the first time three weeks ago, when I initially reported my concern over extortion. The second time was earlier this morning under caution following arrest.
“The arrest was unnecessary as I remain ready to co-operate fully with the investigation that I am confident will end without charge. “I do not intend to say anything further on this matter until the police have completed their inquiries.”
A police spokesperson said: “We can confirm a man was arrested yesterday morning (October 25) on suspicion of rape and possession of controlled substances.
“He has been released on conditional police bail pending further inquiries.”
It is the latest in a string of arrests of sitting MPs.
In May 2022, it was revealed that a Conservative MP, who was not named for legal reasons, had been arrested on suspicion of rape and sexual assault. They have not been charged.
Three years ago, ex-Conservative MP Charlie Elphicke was jailed for two years for sexually assaulting two women.
Last year, former Tory MP Imran Ahmad Khan was jailed for 18 months for sexually assaulting a 15-year-old boy.