Hundreds of people have signed up as members of the Campaign for Nuclear Disarmament since Jeremy Corbyn launched his bid to become Labour leader.

The anti-nuclear group says the rate of signups has increased from about 30 a month before Corbyn began his campaign in June to more than 200 a month now. A spokesman said the membership boost was still gathering pace, with more than 100 new members in the past seven days.

This weekend Corbyn will address the CND’s annual conference in London, which organisers say is the UK’s most important anti-nuclear gathering in a generation.

Kate Hudson, general secretary of the CND, said: “[The] conference takes place at a moment when, for the first time in a generation, the opportunity not to replace Trident collides with a massive popular upsurge against the criminal waste and sheer anachronism of nuclear weapons.

“Austerity has led many more to question the need to spend £100bn on replacing a nuclear weapons system that doesn’t tackle the real security threats we face. Terrorism, climate change, pandemics and cyberwarfare require a fresh approach.”

Corbyn is due to speak at a closed session on Saturday, and the two-day conference will be attended by senior figures from the Green party, as well as Brendan O’Hara, the Scottish National party’s defence spokesman.

Hudson said the growing party political support, combined with the increase in new members and supporters, would make it hard for the government to prevent a genuine debate in parliament over Trident.

“In Scotland, a majority voted for the anti-Trident SNP; the new leader of the Labour party firmly opposes nuclear weapons and is facilitating a national policy debate in his own party,” he said. “The Lib Dems will oppose like-for-like replacement. The Green surge represents further opposition … The government will find it increasingly hard to claim it is acting in the national interest if it cannot garner cross-party support for Trident and when it is at odds with growing public opposition.”

Corbyn’s longstanding opposition to nuclear weapons has provoked criticism from some in the parliamentary party since he became leader last month. After he said he would not authorise the use of nuclear weapons if he were prime minister, the shadow defence secretary, Maria Eagle, described his comments as “unhelpful”. Two leading unions have also expressed their opposition to Corbyn’s anti-nuclear stance.

However, his supporters say the rise in support for the CND shows that Corbyn’s victory is energising political organisations outside parliament, from CND to anti-austerity campaigns.

The former London mayor Ken Livingstone said Corbyn’s election had rejuvenated politics beyond the Labour party. “After the years of the Thatcher/Blair tyranny, I think people realise that they can have an influence in politics again; it is worth getting involved, whether it is environmental groups, CND or the Labour party,” he said.

The UK has four Trident ballistic missile submarines, and a final decision about whether to replace them is due to be taken in 2016. Previously, both the Labour and Tory leaderships were committed to replacing the fleet, a project that is likely to cost well over £100bn over its 30-year lifespan. But now Corbyn has committed Labour to a review of its Trident policy, to be headed by Eagle.

Hudson welcomed Labour’s stance and said the anti-nuclear campaign would continue to gather momentum in the coming months. “Our own organisation has experienced its own surge in membership and we’re preparing for a major national Stop Trident demo ahead of the parliamentary decision in 2016,” she said.