John Humphrys asked his colleague, Jon Sopel: “How much of your salary are you prepared to hand over to Carrie Grace to keep her?”

The leaked clip of John Humphrys making light of the BBC gender pay row reveals “what we’re up against”, according to one of the corporation’s most prominent female broadcasters.

Jane Garvey, the Woman’s Hour host, voiced the displeasure understood to be felt by many women at the corporation after The Times obtained a transcript of Humphrys’ off-air comments.

“Heading into work at the Department of Mixed Messages, formerly known as the BBC #bbcwomen,” Garvey tweeted this morning.

Jane Garvey, the host of Woman’s Hour on BBC Radio 4, has voiced her displeasure at the comments from John Humphrys DANIEL LEAL-OLIVAS/PA

She added that the exchange “reveals, very neatly, what we’re up against” and was a “useful reminder to be ever careful in a room with microphones”.

Jo Swinson, the deputy Liberal Democrat leader, asked whether Humphrys should be banned from presenting stories on BBC gender pay issues, just