London (CNN) The chances of Britain holding a second referendum on Brexit just got higher.

Britain's opposition Labour party voted overwhelmingly Tuesday for a policy that would put a new vote on the table if Prime Minister Theresa May failed to get an eventual Brexit deal through the UK Parliament.

And Labour's Brexit spokesman, Keir Starmer, received rapturous applause at his party's annual conference when he raised the prospect that staying in the European Union would be on the ballot paper.

"Nobody is ruling out 'Remain' as an option," he said.

His comments were significant because Labour has been as divided over the issue as May's Conservative Party. Some Labour MPs represent districts in Britain that voted decisively to leave the EU in the 2016 referendum, and fear losing their seats if there is a general election. The Labour leader, Jeremy Corbyn, is known to be a lifelong Euroskeptic.

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