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Leadership candidate Jess Phillips and deputy leadership candidate Rosena Allin-Khan said Murphy should not be given a peerage while the party is facing 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Hope Not Hate, while the Jewish Labour Movement (JLM) said Murphy’s nomination was “deeply inappropriate” and must be rescinded.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 commission’s role is to advise the prime minister if it has concerns about the propriety of nominees for a peerage, including whether they have good standing with public regulatory authorities.
Corbyn’s decision to nominate his former chief of staff Murphy, as well as former Commons Speaker John Bercow and Labour ex-deputy leader Tom Watson, were initially reported by the Sunday Times.
Phillips told Pieenar’s Politics on BBC Radio 5 Live: “The code of conduct for the Labour leadership competition tells me that I’m not allowed to speak about any members of staff who don’t have a right to reply.
“So I shall just slightly sidestep talking about Karie Murphy, but I don’t think that anybody should given a peerage who is currently under investigation by the EHRC.”
Asked about Murphy’s nomination, Allin-Khan told Sky’s Sophy Ridge On Sunday: “What I do know is that she is currently being investigated by the Equality and Human Rights Commission (EHRC).
“Hope Not Hate said that anyone who is being investigated by the EHRC shouldn’t be recommended for a peerage, so I think that does need to be taken seriously.”
When asked if the nomination would make her “uncomfortable” Allin-Khan said: “I would like to see the outcome of the EHRC report.”
Tony Blair’s former spin doctor Alastair Campbell meanwhile accused Corbyn, who will be replaced by a new leader on April 4, of rewarding Murphy for a “great strategic failure” for presiding over Labour’s catastrophic election defeat from party headquarters.
Corbyn ally and Labour chair Ian Lavery defended Murphy, tweeting: “The abuse, bullying and harassment Karie Murphy receives is quite frankly appalling.
“She is a ferocious fighter for the working class and the most vulnerable!!”
Labour is declining to comment on peerage nominations.