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LONDON (Reuters) - British trade union leaders linked to the opposition Labour Party have agreed to back a second referendum on any Brexit deal reached by the next Conservative prime minister or a no-deal exit, according to a copy of the agreement seen by Reuters.

Labour leader Jeremy Corbyn last month supported holding a second referendum on any Brexit deal, but some in his party want him to unequivocally back a second vote and to commit Labour to campaigning to remain in the European Union.

The unions agreed on Monday that in a choice between a Conservative deal or a no deal and remaining in the EU, they believed Labour should campaign to remain, the text of the agreement shows.

Trade unions are Labour’s biggest financial backers and the decision will add to pressure on Corbyn, who has come under fire for trying to keep both “Leave” and “Remain” sides happy, to move the party to supporting remaining in the EU.

On Sunday, the party’s finance spokesman John McDonnell told BBC TV he wanted to campaign to remain if there were a second referendum.

Asked about the union agreement, a Labour source said Corbyn had been working to unite the party and wider Labour movement around a common agreed position.

The text of the union agreement said that if a national election were called, Labour’s position should be that it would negotiate its own exit with the EU and then that deal should be put to the public in a second referendum.

In that scenario, the choice on the ballot paper would be between Labour’s deal and remaining in the EU, the unions said, and how Labour campaigned in a second referendum would depend on the deal negotiated.

A Conservative spokesman said: “Labour promised to respect the Brexit vote, but re-running the referendum and backing remain would be an attempt to frustrate Brexit and ignore the democratic mandate to deliver it.”