The Democratic Unionist Party’s 10 MPs backed the government in Tuesday’s Commons vote, in which Boris Johnson suffered his first defeat as PM.
The Commons voted 328 to 301 to take control of the Brexit agenda, meaning they can bring forward a bill seeking to delay the UK’s exit date.
Independent unionist MP Lady Hermon voted against the government.
Mr Johnson has said he will seek to trigger a general election if MPs vote for legislation to block no deal.
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In total, 21 Tory MPs, including a number of ex-cabinet ministers, joined opposition parties to defeat the government.
Ahead of the vote, the DUP said it would not vote in favour of the motion, as it believed it would weaken the government’s negotiating hand with Brussels.
After the historic vote, Mr Johnson said he did not want an election – but that if MPs backed legislation forcing his hand – then the public would have to decide whether he, or Jeremy Corbyn should be tasked to deliver Brexit.
DUP chief whip Sir Jeffrey Donaldson told BBC Newsline that he believed an election was now almost certain.
He added that he believed the government would struggle to get two-thirds of MPs to vote in favour of triggering an election, under the terms of the Fixed-Term Parliament Act.
Meanwhile, the Irish government has said it is giving its no-deal Brexit contingency plans “top priority”.
The cabinet met on Tuesday night to discuss the latest developments in Westminster, and said it noted that a no-deal Brexit is “increasingly likely”.
The legal default position is that the UK is due to leave the EU on 31 October, unless an extension is granted.
The Irish government said it has issued an additional “call to action” to ensure that businesses are ready for the new regulatory requirements in the event of a no-deal Brexit.