Jeremy Corbyn has told his Labour critics that his mandate to lead the party will stretch beyond Westminster if he wins the contest to succeed Ed Miliband. Amid rising concern among established Labour figures at the apparently unstoppable momentum behind the veteran leftwinger, Corbyn said his campaign has captured a public mood against austerity also seen in Spain, Greece and the US.

Corbyn is facing suggestions that he would not have a mandate to lead the party after only making it on to the ballot paper at the last minute because other Labour MPs “lent” him their votes to promote a debate about the party’s future.

But in an interview with the Guardian, Corbyn made it clear he was rising above personal attacks: “The mood is there and we happen to be in the middle of it. We are not doing celebrity, personality, abusive politics – we are doing ideas. This is about hope.”

Fears of a Corbyn victory prompted the former home secretary Alan Johnson to endorse Yvette Cooper this week with a call to “end the madness” and have led to warnings that activists on the hard left are seeking to infiltrate the leadership contest. Labour party officials confirmed that 250 former candidates and members of parties to the left of Labour have signed up to allow them to vote in the leadership contest.

Corbyn said he warned the party early on in the contest about the new system. But he thinks the number of people who want to disrupt the process will be small. “The numbers don’t stack up,” he said. “The entryism, if anything, is of enthusiastic young people. We can all be happy about that.”

The deadline for signing up to take part in the vote is next Wednesday, two days before ballot papers are sent out. The new leader will be announced on 12 September.

Why are young people rallying behind Corbyn? Guardian

Corbyn admitted that he was surprised by his success, which has seen him address 43 packed public meetings across the country, resulting in a severe cold that has affected his hearing. Of his support, he said: “It has grown a lot faster than anyone could have understood or predicted or expected. But it has shown there is such latent good, such latent enthusiasm, such latent optimism in people.”

The MP for Islington North, who invariably has to leave meetings to address supporters left out in the street, said that the large number of people outside the normal world of politics would give him a mandate to lead Labour. “The parliamentary Labour party is only part of the party,” he said. “This election is about the participation of a very large number of people. It is the most open electoral process Labour has ever undertaken. I am not sure that when those who designed this system designed it, they realised what was going to happen.”

He added: “I recognise that there are a lot of people that come together in this and want to take part in discussion and debate. It is a mandate.”

Corbyn also made clear that he would not give David Cameron a “blank cheque” in his EU negotiations as he made it clear that the prime minister cannot promote a “free-market European economy that tears up environmental protection, social protection and workers’ rights”. Asked what he would do as leader if the prime minister ignored his demands in the negotiations, Corbyn said: “At that point we go back to our own party and our movement, and decide what we do. We don’t give a blank cheque now in advance for Cameron to do whatever he wants to do.”

Corbyn strongly defended plans by his economic adviser, Richard Murphy, for a people’s quantitative easing to fund a national investment bank. He denied it would stoke inflation because the British economy is growing “very unevenly”. He also pointed out that he is committed to eliminating the budget deficit, though he would not do this on the “arbitrary” timetable set by the Tories.

“The idea that we are some kind of obscure deficit denier is a total nonsense. Why is [Joseph] Stiglitz welcoming what we are saying?”

John Harris charts Jeremy Corbyn’s rise to Labour leadership frontrunner Guardian

Corbyn, who is opposed to expanding the British military involvement in the campaign against Islamic State, offered assurances that, as leader of the opposition, he would accept invitations from the prime minister to attend meetings of the National Security Council. “The only responsible thing to do is to take part in those discussions. But you’d have to set some ground rules in advance. Does it mean you are going to agree with the outcome? No, of course it doesn’t, as we showed over the Syria vote.”

Leaders of the opposition are briefed on intelligence matters on what is known as “privy council terms”. But Corbyn has said he was not sure whether to accept the customary invitation for the leader of the opposition to join the privy council, which would mean that he would be known as the Right Honourable Jeremy Corbyn MP. “I am quite capable of having private discussions with anybody whether I have got a handle on my name or not,” he said. “I have been involved in plenty of those discussions as an MP. A handle doesn’t give you authority.”