"I think it would be inconceivable for any Prime Minister to seek to stand in the way of a referendum if that's what the Scottish parliament voted for," Sturgeon told broadcasters after meeting new British Prime Minister Theresa May.
British PM May gets down to work under Brexit pressure
Sturgeon wants Scotland to stay in the EU, and Scots as a whole voted to stay in the bloc in Britain's June 23 referendum.
May told broadcasters earlier that Scots had had their chance to vote for independence in 2014, but she would not formally trigger divorce talks with the European Union until a "UK approach" had been agreed.
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