In a highly unusual move, the Labour leader has reportedly stepped in to nominate Mr Bercow for a seat in the Lords after Mr Johnson broke with convention by failing to put forward the former speaker for a peerage.
His decision to nominate Ms Murphy has also sparked a major row, as her role in the handling of Labour’s antisemitism complaints is still being investigated by the Equality and Human Rights Commission (EHRC).
The equalities watchdog is carrying out a major probe into antisemitism in Labour, which is expected to report within the coming months.
Mr Bercow’s nomination is likely to anger Conservative Brexiteers, who saw him as a block to passing Brexit legislation over the past few years.
The details emerged in a leak of Mr Corbyn’s nominees for the upcoming dissolution honours list, obtained by The Sunday Times, which comes after the dissolution of a parliament for an election.
Labour sources failed to deny Mr Bercow and Ms Murphy were on Mr Corbyn’s list, which is also said to include Tom Watson, the party’s former deputy leader, who stood down at the election.
Ms Murphy’s inclusion stoked particular anger among Labour MPs, as she was also seen as playing a key role in the party’s disastrous election result.
One Labour MP told The Independent: “Corbyn’s leadership ends in a most appropriate way: with the stench of cronyism, failure and hypocrisy following Lady Murphy in her ermine all the way down to the red benches.”
Leadership candidates Jess Phillips and Rosena Allin-Khan both said Ms Murphy should not be given a peerage until the probe is complete, while the Jewish Labour Movement (JLM) said the nomination was “deeply inappropriate”.
Ms Allin-Khan told Sky’s Sophy Ridge On Sunday programme: “I personally don’t know Karie Murphy well at all. What I do know is that she’s currently being investigated by the EHRC. And I made clear yesterday that as deputy leader I would take onboard every single recommendation by the EHRC.
“Hope Not Hate said that anyone being investigated by the EHRC shouldn’t be recommended for a peerage. So I do think that needs to be taken seriously.”
Ms Phillips said she would not comment on staff but added: “I don’t think anybody should be given a peerage who is currently under investigation by the EHRC.”
The JLM tweeted a statement saying Ms Murphy’s nomination was “deeply inappropriate and must be rescinded immediately”.
“Jeremy Corbyn is using his final weeks in office to reward failure,” it added.
But Ian Lavery, the Labour chairman, came to Ms Murphy’s defence, saying the abuse she received was “frankly appalling”.
“She is a ferocious fighter for the working class and the most vulnerable,” he added.
No date has been set for the publication of the honours list.