First Minister Nicola Sturgeon vowed to make Trident renewal an “election issue” in an impassioned speech to thousands of peace campaigners in Trafalgar Square.

Urging activists to “stand up and be counted”, the leader of the Scottish National Party said her opposition to the UK’s nuclear missile system had grown since joining the Campaign for Nuclear Disarmament (CND) a full year before she signed up as an SNP member in 1986. Yesterday’s demonstration is thought to be the biggest of its kind for a generation.

Sturgeon also baited the Conservative government over a planned vote in parliament on the renewal of Trident, which she said is “one of the most significant decisions to be taken by the UK Parliament this year”.

After marching through the streets of London flanked by Plaid Cymru leader Leanne Wood, Green Party MP Caroline Lucas and several SNP MPs, the First Minister addressed a CND rally.

Among tens of thousands of demonstrators who turned out was Labour Party leader Jeremy Corbyn, actress and political activist Vanessa Redgrave, writer and anti-war activist Tariq Ali, comedian Francesca Martinez and representatives of the Public and Commercial Services Union and the Stop the War Coalition.

Sturgeon said: “There have been reports that the Tories have been fretting about when to hold their parliamentary vote on Trident renewal. They were worried that opponents of Trident might make it an election issue over the next couple of months. Well, we have a message for them: you bet we’re going to make it an election issue.”

The UK’s four nuclear-armed submarines are based at Faslane on the Clyde from where they are sent out to patrol the world’s seas.

Sturgeon said: “These are weapons of unspeakable power and brutality, capable of unleashing terror and human suffering on a simply unimaginable scale – and the UK Government is intent on basing another generation of them in Scottish waters, against the views of the majority of Scotland’s political, civic and religious representatives.

“But this is an issue affecting people the length and breadth of the UK – and all of us who fundamentally believe in a nuclear-free world now have to make the case.

“All of us must leave here today and keep nuclear disarmament at the top of the agenda. It’s time for all of us to stand up and be counted.”

The Ministry of Defence has estimated that acquiring four new submarines to carry the Trident deterrent will cost £31 billion over the course of the 20-year procurement programme, with a further £10 billion set aside to meet any additional unexpected cost increases. Other estimates put the price of the project closer to £167 billion – a figure described as “exorbitant” by Sturgeon.

She said: “Like everybody here, I have been campaigning for nuclear disarmament for a long time. And like everybody here, as the world has changed, my conviction that we must rid ourselves of these weapons of mass destruction has only become stronger. The financial cost – already exorbitant – is spiralling completely out of control.

“And the defence argument – already illogical – is now completely indefensible. So the moral argument for disarmament – already powerful and persuasive – is now stronger than ever.”

Labour leader Jeremy Corbyn, who addressed the rally after Sturgeon, said: “We live in a world where so many things are possible. Where peace is possible in so many places. You don't achieve peace by planning for war, grabbing resources and not respecting each other's human rights.

“Today's demonstration is an expression of many people's opinions and views. I'm here because I believe in a nuclear-free Britain and a nuclear-free future.”

Corbyn has long campaigned for unilateral disarmament but faces a showdown with some of his shadow cabinet, including shadow foreign secretary Hilary Benn, who said he believed in multilateral action.

The shadow cabinet has yet to decide how it will handle any Commons vote on Trident, expected later this year, ahead of the recommendations of a review of the party's existing support of renewal led by unilateralist shadow defence secretary Emily Thornberry.

Meanwhile, Scottish Labour leader Kezia Dugdale’s spokesman described her as a “multilateralist”, despite party members voting against Trident renewal at conference.

“Scottish Labour opposes the renewal of Trident, but the money saved must be spent on ensuring the thousands of people whose jobs currently depend on the deterrent in Scotland are found alternative work,” added the spokesman, who didn’t want to comment on yesterday’s demonstration.

A UK government spokeswoman also declined to comment on the demonstration but Scottish Conservative MSP Alex Johnstone said: “It’s no surprise to see Nicola Sturgeon and Jeremy Corbyn linking arms at an anti-Faslane rally. They don’t care that thousands of jobs in Scotland depend on Trident, nor that it helps safeguard Britain’s place in the world.

“It would be madness to scrap Trident at a time when rogue states are pursuing nuclear weapons. Many surveys have shown people in Scotland are happy to have Trident here, and would rather it was renewed.”

A spokeswoman for the Ministry of Defence said: “The UK's independent nuclear deterrent is the ultimate guarantee of our nation's safety which is why the government is committed to maintaining it. We estimate costs will amount to around 0.2% per year of government spending - a small price to pay to ensure the security of British citizens.”