Members of the GMB union are believed to have backed Owen Smith as Labour leader in a consultative ballot.
The union, one of the biggest affiliated to the party, asked its 600,000-plus members if they wanted to support Mr Smith or Jeremy Corbyn.
Around 30,000 GMB members are eligible to vote in the leadership election, but the union wanted to gauge the feeling of all its members.
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The GMB represents workers on the Trident nuclear weapons programme.