Jeremy Corbyn has lost his fourth shadow minister in a week, as one of Britain’s most powerful trade union leaders warned that the Labour leader will have “another shock coming” if he tries to change party policy on the Trident nuclear weapons system.

Shadow attorney general Catherine McKinnell said she was stepping down partly because of the difficulty of reconciling her role with family commitments. But in a letter to Mr Corbyn, she also expressed concern over internal conflicts and the direction of the party since he became leader.

“As events have unfolded over recent weeks, my concerns about the direction and internal conflict within the Labour Party have only grown, and I fear this is taking us down an increasingly negative path. I feel that I would like to channel my energy constructively, into making positive changes for my constituency,” she wrote.

Three shadow ministers resigned from the front bench last week following Mr Corbyn’s shadow cabinet reshuffle, in which he sacked two spokespersons and replaced Maria Eagle with Emily Thornberry as shadow defence secretary. Unlike Ms Eagle, Ms Thornberry shares the Labour leader’s opposition to renewing Trident.

Mr Corbyn said yesterday that Labour’s National Executive Committee would consider changing party rules to make it easier to reverse current policy, which backs renewing the nuclear weapons system.

“I want members to have a big say in it, whether that comes as a vote of individual members or a vote at conference . . . I haven’t made up my mind about that,” he told the BBC.

A few hours later, however, Sir Paul Kenny, leader of the GMB union, warned that adopting a policy of unilateral nuclear disarmament could threaten the livelihood of many of his members whose jobs depend on Trident.

“If anybody thinks that unions like the GMB are going to go quietly into the night while tens of thousands of our members’ jobs are literally swannied away by rhetoric, then they’ve got another shock coming,” he said.

Kenny dismissed Mr Corbyn’s suggestion that his overwhelming victory in the Labour leadership election gave him a mandate to change party rules over how policy is determined.

He said that the GMB would mobilise workers at 50 defence industry sites across the UK to oppose any effort to scrap Trident.

“The Labour party policy at the moment, reaffirmed at the party conference recently, is the renewal of Trident. Jeremy is perfectly entitled to say he wants to change that policy. But he needs to go through the same democratic process that arrived at that policy in the first place,” he said.

Earlier, Mr Corbyn said that Labour’s policy on Trident should be informed by the party’s longstanding support for the nuclear non-proliferation treaty, which Harold Wilson signed up to in the 1960s.

“If we want to live in a nuclear-free world, we have to recognise that we have to make a contribution to it,” he said.

“Renewing Trident, in my view, goes against the fundamental spirit of the nuclear non-proliferation treaty, which requires the five declared nuclear weapons states not to renew their weapons systems.”