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Defiant Jeremy Corbyn tonight hits back as the anti-Semitism row threatens to engulf Labour, warning his MPs: “I am carrying on.”

Speaking to the Mirror ahead of Thursday’s local elections, the leader dismissed calls to quit if Labour perform badly and vowed to face down any leadership challenge.

“If there is one, there is one – but I’m not having sleepless nights about this,” Mr Corbyn said.

“I was elected with a very big mandate to do the job, and I am doing the job.”

And issuing a direct message to Labour MPs plotting a coup attempt if the party loses seats, Mr Corbyn told them: “Respect the mandate. Respect the wishes of party members.

“Recognise, get out there, campaign as you’ve never campaigned before.”

But with three more Labour councillors suspended today over charges of anti-Semitism, Mr Corbyn risked further angering his critics by denying the party has a problem.

“No, there is not a huge problem,” he said.

(Image: Andy Stenning/Daily Mirror)

Read more: Labour suspends 3 councillors within hours

“What there is is a very small number of people that have said things that they should not have done.

“We have therefore said they will be suspended and investigated.”

And he refused to condemn left-wingers who carried banners of murderous Communist dictator Josef Stalin at the May Day rally he addressed in London on Sunday afternoon.

“You can’t stop people holding them up,” Mr Corbyn said. “I’d rather they didn’t.

“The London May Day rally is not organised by the Labour Party . It’s not in our hands.”

Mr Corbyn has faced arguably the toughest week of his leadership following the suspension of Labour MP Naz Shah, close ally Ken Livingstone and a succession of local councillors for alleged anti-Semitic comments.

On Friday night he set up a special commission to investigate anti-Semitism and other forms of racism within the Labour Party, headed up by charity campaigner Shami Chakrabarti.

Asked if the very fact such a commission is needed is itself evidence of a problem, Mr Corbyn said: “No, it’s not evidence.

“It’s evidence of our absolute determination to deal with a problem in a very open way. I invite other parties to do exactly the same.”

(Image: Andy Stenning/Daily Mirror)

The Labour leader added that he has “spent my whole life opposing racism”

and is clearly unhappy at the accusations now being thrown his way.

“My parents came from a generation that were there in Cable Street (fighting fascism in the 1930s). That is the whole tradition I have come from,” he said.

“I find it obviously wrong that people should accuse me of anything like that, and therefore we’ve taken the action that we have.”

But does he understand the concerns of members of the Jewish community and many of his own MPs about some of the people he has associated with, including members of Hamas and Hezbollah?

“I’ve been involved in political activity in all my life. I have therefore met with people with whom I profoundly disagree in order to promote a dialogue,” he said.

“The whole point about politics is about building that sense of dialogue.”

He illustrates the point by highlighting the bridge-building work of historic figures from Nelson Mandela to Tony Blair .

“You have to reach out,” he said. “It is a political process that brings about peace in the end.”

(Image: Andy Stenning/Daily Mirror)

He also dismissed a warning from Labour’s London Mayoral candidate Sadiq Khan that the anti-Semitism row had damaged his own chances of winning back control of the capital on Thursday.

“I don’t think it’s damaged his chances at all,” Mr Corbyn said.

“We acted very quickly on this, we set up the commission, and I would invite everyone who wants better housing, better transport and a greener cleaner London to vote for Sadiq.”

The Labour leader is rightly furious at the shameless campaign run by Tory candidate Zac Goldsmith , who has highlighted Mr Khan’s Muslim background and tried to paint him as ‘extreme’ and a threat to London.

“I’m appalled and alarmed by it. The way in which they are trying to denigrate Sadiq for his faith... He’s a figure that wants to unite not divide,” Mr Corbyn said.

“I am surprised and disappointed. Zac Goldsmith is somebody I always assumed was a sort of liberal Tory, good on the environment and everything.

“He’s run a depressingly negative, nasty campaign, personally vilifying Sadiq Khan. It’s no way to conduct politics. He is diminished in my view.”

Despite the Tory campaign Mr Khan remains the hot favourite to succeed Boris Johnson as London Mayor, and could prove the only bright spot for Mr Corbyn on polling day.

Independent forecasters have predicted Labour could lose up to 150 council seats in England, face wipe-out in Scotland at the hands of the Scottish National Party and lose control of the Welsh Assembly.

Critics on his own backbenches have said it would be a “betrayal” for Labour to lose even a single council seat and some are hoping to use the results to trigger a coup.

But Mr Corbyn said: “There are no goals, no targets - the best result we can get.”.

And asked if any result would be so bad he would quit, he replied: “No. I am carrying on.”

The Labour leader pointed out he was only elected eight months ago with an overwhelming majority and made clear he will stand again if he faces any challenge.

(Image: Andy Stenning/Daily Mirror)

“I was elected on a mandate from a very large majority of members and supporters of the party. I intend to carry out that mandate,” he said.

“The Parliamentary Labour Party are a very important part of the Labour movement - but it’s not the only part.”

His ongoing popularity among the grassroots was evidenced again yesterday by the hundreds of people who turned out to hear him speak at another May Day rally, in Burnley.

“I think that connecting with the active grassroots of the Labour movement is very important,” he said.

“The tradition of Labour May Day rallies is a huge one. There are people looking for a sense of community through the Labour Party.”

So why does he think previous leaders have been reluctant to address the London May Day rally, as he did on Sunday afternoon?

“I think there’s been too much nervousness about where we come from,” he said.

“I think we should be proud of were we come from. It’s part of our tradition.”

Looking back on his first eight months in charge Mr Corbyn immediately listed “changing the nature of Prime Minister’s Question Time” as one of his proudest achievements.

He added: “I’ve done far more reaching out and campaigning than many others. I spend two or three days a week on the road every week, travelling around the country.

“I meet vast numbers of people – I find that very interesting, I pick up lots of ideas that way.”

And he highlighted wins in the Commons on cuts to tax credits, disability benefits and Sunday trading.

But what about a biggest mistake?

“I’m sure I’ve made loads,” he smiles.

“There’s been a few - but that’s between me and my memory.

“There’s plenty of other people analysing my mistakes, there’s no need for me to add to that.”

Mr Corbyn was speaking to the Mirror today after addressing a rally in Burnley.

Hours later a member of his shadow cabinet reiterated the need to tackle anti-Semitism in the party.

Shadow education secretary Lucy Powell told Channel 4 News: "There clearly is an issue with anti-Semitism in the Labour Party - otherwise we wouldn't have spent the best part of the last six or seven days talking about it.

"I think it is a very small element within the Labour Party and probably a small element in wider society as well.

"And that's why we are taking swift action to root it out."

Asked about Mr Livingstone's future within the party, she added:

"That will be a matter for the National Executive Committee who will look at that and they will come to their own view.

"I think it's very, very difficult to see a circumstance where his suspension would be lifted and he would be readmitted."