The peer said the Labour leader would be “wise” to offer his MPs a free vote in a looming Commons showdown – but if he did not, frontbenchers who favoured broadening the military action should abstain and challenge him to sack them.
Former Sheffield Brightside and Hillsborough Labour MP Lord Blunkett also warned that the electorate was “bewildered” by Mr Corbyn’s approach and he had a “very short period of time” to show he “knows how to be prime minister”.
Interviewed on the BBC Radio 4 Today programme, Lord Blunkett joined calls for ex-London mayor Ken Livingstone to be removed from his role co-chairing the party’s defence policy review after he suggested that shadow defence minister Kevan Jones needed “psychiatric help”.
The peer said Mr Corbyn was experiencing the problems of moving “from dissident oppositionist within eight weeks to being the leader of a major party whose hopes are, and whose supporters’ hopes are, for a Labour victory – not for a permanent revolution where you become simply a campaign group”.
“Eight weeks on there are signs that Jeremy has got one or two of those things, including the way he has handled himself at PMQs, including letting people like [shadow home secretary] Andy Burnham handle the investigatory powers draft Bill really sensibly,” he said.
“But then of course he makes appointments – just talking about Ken Livingstone – and people around him who have an entirely different view of which way the Labour Party should proceed.”
Lord Blunkett said he wanted “sane, sensible people” to do something that was currently “totally counter-intuitive”.
“I want them to join the Labour Party,” he said. “I want them to join it so that their voice of sane, sensible people, wanting radical policy, can get the Labour Party into a position with those radical policies but in a credible situation to win the next general election.
“I think [the public] are bewildered, and Jeremy has got a very short period of time – in politics short spaces of time are 18 months/two years – to actually demonstrate that he wants to be prime minister, that he knows how to be prime minister, and, if he was, people would feel confident in what he said and he did.
“Eight weeks on, nearly nine weeks on, I think he has got a lot to learn.”
The ex-Cabinet minister said he did not believe shadow ministers concerned about Mr Corbyn’s approach should quit.
“Those people who have signed up to the shadow portfolios, I would advise, seeing as you have done so, stay in there,” he said.
“This is not the time to hive off bit by bit – not least on the issue, which I happen to be in favour of, of changing our line in terms of bombing alongside the French and the Russians and the Americans across the non-existing border between Iraq and Syria.”
Lord Blunkett said if the leadership had “any statescraft at all” they would give MPs a free vote on the issue.
Asked what frontbenchers should do if Mr Corbyn did impose a whip, the peer said: “I would abstain and challenge Jeremy Corbyn to sack them.”