Labour's deputy leader has warned trade union chiefs of a backlash from their members over Jeremy Corbyn's decision to vote against renewing the UK's nuclear deterrent, Trident. Tom Watson said the leaders of Unite and the GMB Union, Len McCluskey and Tim Roache, could face "consequences" for backing the unilateralist.

"There are tens of thousands of members of Unite and the GMB who work in the defence sector or in civil or military nuclear sector or in aerospace, whose jobs depend on this programme going through," Watson told BBC Radio 4's World at One programme.

"You have McCluskey strongly supporting Corbyn, who will be voting against the Trident programme tonight [18 July], which will put many defence workers in Unite out of their jobs if he gets his way."

Watson said he would be backing the renewal of the continuous-at-sea nuclear weapon system alongside the government when he votes on the issue later. But shadow foreign secretary Emily Thornberry and shadow defence secretary Clive Lewis have urged Labour MPs to abstain from voting.

Thornberry's defence policy review, which included the party's stance on Trident, was originally schedule to be published a week after the EU referendum. However, the Brexit result meant that it has been delayed. The postponement means Labour's pro-renewal commitment in its 2015 general election manifesto remains party policy.

The wider labour movement is also split on the issue. Unite and GMB, despite their support for Corbyn's leadership, back renewing Trident, while fellow major trade union Unison opposes it.

"It's not acceptable to play politics with our members' livelihoods. Ministers and MPs need to stop messing about and get on with making the decision to renew. Tens of thousands of workers' jobs are on the line and they've been kept waiting by political point scoring and Westminster bubble politics for too long," Roache argued.

"Labour's policy is to have a continuous at-sea deterrent. It beggars belief that so many MPs jump up and down shouting about party democracy, but aren't batting an eyelid about voting against the democratic will of their own party conference when the line doesn't suit."

But Dave Prentis, the general secretary of Unison, said his union would never support renewing Trident. "What the British economy needs now is real investment in our public services – not years of cuts, and certainly not a nuclear weapons system designed for the Cold War era," he declared.

"If there are tens of billions of pounds available for the government to spend, then let's invest it in our schools, hospitals and social care system. Let's give public sector workers the pay rise they all deserve – and boost the economy at the same time.

"But let's stop accepting the argument that there's always more money for bombs we hope will never be used, but never enough money for decent pay, decent jobs and decent services."

The row comes as Corbyn, who won almost 60% of the vote in Labour's 2015 leadership contest, faces a leadership challenge from former shadow cabinet minister Angela Eagle and Owen Smith.

The left-winger is automatically on the ballot after a ruling from the party's National Executive Committee, while Smith and Eagle will each have to attract 51 nominations from Labour MPs and MEPs before nominations close on Wednesday. The winner of the contest will be announced on 24 September in Liverpool.