Deputy Labour leader Ms Rayner said Mr Johnson had a responsibility to investigate any “serious” claim against an MP prior to making such a significant appointment.
“In terms of Chris Pincher and the Prime Minister, look, I mean it sounds like a logical thing to do, but you ask, don’t you?,” Ms Rayner said at the Institute for Public Policy Research (IPPR) think tank.
“‘There’s rumours flying around, can I ask the question – is there anything that you’ve done that could be considered…?’
“And I would have investigated (the rumours).
“If I was the Prime Minister and somebody had said that, I would have said – ‘these rumours, that’s really serious, I want it investigated, I want to find out if there’s any truth to it’.
“I think that’s a logical thing.
“If you work in HR, if you’re a trade unionist or anyone else and someone says ‘oh, I’ve heard this rumour’, I’d want to find out and see whether that rumour is correct or not, rather than just say, ‘well, it’s just a rumour, I’ll give you a top job over (the) welfare of other MPs’, to be honest.
“So I find it speaks to the character of Boris Johnson, if that’s the way he felt to deal with that at that time.”
Downing Street confirmed on Monday that Mr Johnson knew of concerns about Mr Pincher’s conduct when he made him deputy chief whip in February.
Mr Pincher plunged the Government into a new crisis when he dramatically quit last week over allegations he groped two men at a Conservative private members’ club.
He had previously resigned from the whips’ office in 2017 over claims he made unwanted advances to a young activist, but was later reinstated after being cleared by an internal Conservative Party investigation.
Over the weekend, however, details emerged in the press of further claims about alleged sexual advances to men – including two fellow Conservative MPs – over a period of years.
Mr Pincher has denied the allegations to the newspapers which carried them.
However, Mr Johnson’s spokesman said the Prime Minister had been aware of the “speculation” there had been about Mr Pincher over a number of years when he made him deputy chief whip.
Ms Rayner said it was the PM’s job to create an environment “where people can come forward and feel supported”.
“And it’s Boris Johnson that is the problem and he should have done something about it,” she said at IPPR.
“And it’s not plausible to me to turn around and say: ‘Well, it was just a rumour’.
“It’s your job to go out and find out if there’s any truth to that rumour and create an environment where people can come forward and feel supported and feel that that something will be done about it, not that the perpetrator will be promoted.”