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The Labour leader is said to have earmarked the controversial ex-Commons speaker for a peerage in his outgoing parliamentary dissolution honours list.
But Boris Johnson’s official spokesperson said it was a “longstanding convention” that opposition leaders only nominate peers representing their own party.
His comments suggested No.10 could block the appointment unless Bercow, a former Tory MP, switches his allegiance to Labour.
Johnson is expected to break with tradition by refusing to nominate the ex-speaker, such is the anger over his handling of 2019’s Brexit debates and votes in the Commons.
It is understood that Downing Street has not yet seen any opposition nominations list.
The PM’s spokesperson told reporters: “It is a longstanding convention that leaders of the opposition can nominate individuals representing their party for peerages.”
Corbyn’s honours list, as reported by the Sunday Times, has proven controversial.
The inclusion of his former chief of staff and Labour elections chief Karie Murphy has prompted a backlash from senior Labour figures.
Leadership candidate Jess Phillips and deputy leadership candidate Rosena Allin-Khan said Murphy should not be given a peerage while the party is facing an investigation over alleged anti-Semitism by the Equality and Human Rights Commission (EHRC).
That view was echoed by the anti-racism charity Hope Not Hate, while the Jewish Labour Movement (JLM) said Murphy’s nomination was “deeply inappropriate” and must be rescinded.
The JLM said it had written to the Lords appointment commission to raise concerns about Murphy relating to concerns about disciplinary processes and “botched handling of anti-Semitism” in the party. The party did not respond to requests for comment regarding the JLM’s claims.
Labour ex-deputy leader Tom Watson is also reported to be on the list.
This article originally appeared on HuffPost.