One insider said the BBC co-workers of Mr Humphrys were furious.
He said: “There are very hard-working people on shows like Today who earn less than one-tenth of what John Humphrys is on, and they hear him say this.
“Studio managers, engineers and producers are incredibly skilled. If you treat them nicely, they tend to treat you nicely too. I’m afraid one or two of them have been on the receiving end from John and may have decided enough was enough.”
Woman’s Hour presenter Jane Garvey was among those who went public with their distaste.
She said the exchange “reveals, very neatly, what we’re up against” in the battle for women at the Beeb.
Last night Ms Garvey said: “It was a private conversation and I have a certain amount of sympathy for the manner in which this has been exposed, whilst also feeling a bit let down. The man is a brilliant broadcaster and an incisive interviewer, and I’m disappointed by this.”
A BBC spokesman said: “John Humphrys is bound by the same rules on impartiality as all other BBC presenters.”