The BBC has resisted pressure to take formal action over John Humphry’s jokes about the corporation’s gender pay gap as the former presenter Miriam O’Reilly accused the corporation of “censorship” amid escalating anger within the newsroom.

Following a leaked off-air conversation between Humphrys, a presenter on Radio 4’s Today programme, and the BBC North America editor, Jon Sopel, about the former China editor Carrie Gracie, the BBC said the comments did not break its editorial guidelines as they were not explicitly campaigning about an issue.

However, O’Reilly, who was due to appear on Today to talk about equal pay, claimed she was stood down from appearing on the programme because she questioned a producer on Thursday about Humphrys’ impartiality to discuss the issue due to his joking earlier in the week. Humphrys – who earned between £600,000 and £649,999 last year – was due to be presenting on the day she was scheduled to speak.

Miriam O’Reilly: ‘The BBC have got it completely wrong here.’ Photograph: Graham Turner/The Guardian

His comments – in which he made light of Gracie’s decision to leave her post as China editor after she learned that male colleagues, including Sopel, were earning significantly more than her – are believed to have been made on Monday but were leaked on Wednesday and O’Reilly told the producer she had heard them.

O’Reilly, who won a landmark case against the BBC over ageism, said: “I think that was enough for him to be taken off air. He was contemptuous and I was just sickened by it.”

She believes these views, expressed to a Today producer on Thursday, led to her being told she was no longer needed as a guest because of the “nature of news”.

“Minutes after I told the producer that I had heard the tape I was stood down,” said O’Reilly. Asked whether her views led to the change of mind, she said: “I’m absolutely convinced about it, there no doubt in my mind that’s why.”

O’Reilly added: “It’s not what you expect from the BBC, it’s censorship … This has been a PR disaster and an extraordinary mess. The BBC have got it completely wrong here. It’s staggering how wrong they’ve got it.”

A BBC spokesman said: “The Today programme often makes changes to schedules and contributors in the run-up to broadcast. This item became a much broader discussion about social change and consequently Afua Hirsch was a more suitable guest to talk about the wider issues. It’s wrong to suggest anything else.”

But Hirsch tweeted that she would not have agreed to appear on the programme had she known O’Reilly was being dropped from the programme:

So my name is being invoked to justify dropping @OReillyMiriam from @BBCRadio4 . Knew nothing about this and, for the record, I stand with all my female colleagues on #EqualPay & every other injustice we face. Wld I have agreed to do the interview if I’d have known this? No. https://t.co/sQVxNxcRYb — Afua Hirsch (@afuahirsch) January 12, 2018

O’Reilly’s comments were echoed by another female presenter, who told the Guardian it was “frustrating” that it appeared that male colleagues were able to discuss gender pay having voiced opinions about it, but female journalists were told they could not discuss the issue on-air because they had showed online support for Gracie.

In Humphry’s exchange with Sopel he can be heard telling him: “The first question will be how much of your salary you are prepared to hand over to Carrie Gracie to keep her, and then a few comments about your other colleagues, you know, like our Middle East editor [Jeremy Bowen] and the other men who are earning too much.”

Sopel replies: “I mean, obviously if we are talking about the scope for the greatest redistribution I’ll have to come back and say well yes Mr Humphrys, but …” to which Humphrys responds: “And I could save you the trouble as I could volunteer that I’ve handed over already more than you fucking earn but I’m still left with more than anybody else and that seems to me to be entirely just – something like that would do it?”

He continues: “Oh dear God. She’s actually suggested that you should lose money – you know that, don’t you? You’ve read the thing properly have you?”

Humphrys defended the conversation in the Sun as “silly banter between old mates”.