Website ‘Politics Home’ reports that Northern Ireland Secretary Karen Bradley issued the warning at Tuesday’s meeting of the Cabinet.
The website claims that Ms Bradley said a border poll on the reunification of Ireland was “far more likely” if the United Kingdom crashes out of the European Union without a withdrawal agreement.
Under the Good Friday Agreement, a referendum on Irish unity can only be called by the Northern Ireland Secretary if there is evidence that a majority in the province would support a United Ireland.
One Cabinet source told Poltics Home: “The view was that a border poll in Northern Ireland was all-but inevitable if there is a no-deal Brexit because Sinn Fein would demand it straight away.
“The Secretary of State (Karen Bradley) would have no choice but to call one.”
Sinn Fein President Mary Lou McDonald, speaking to reporters in Brussels on Wednesday, said: “We believe we’re in a process now in achieving a referendum on Irish unity.”
She added that in the event of a no-deal Brexit, Sinn Fein will push the British Government to call a border poll.