The Prime Minister was urged by Tory MP Stephen Kerr to “firmly” tell the First Minister the UK Government was against such a poll.
Mrs May replied at Prime Minister’s Questions: “He is absolutely right.
“As he points out, Scotland held a referendum in 2014. It was legal, it was fair, it was decisive and the people clearly voted for Scotland to remain part of the UK.
“But more than that, at the last general election the people of Scotland again sent a very clear message that they do not want a second divisive referendum.
“But the SNP sadly are out of touch with the people of Scotland and they haven’t yet heard that message.
“The last thing we want is a second independence referendum. The UK should be pulling together, not being driven apart.”
Stirling MP Mr Kerr had asked: “May I say, as a proud Scot, that the UK is the most successful political union the world has ever known.
“Does the Prime Minister agree with me that when Nicola Sturgeon demands a second independence referendum only four years after we had the last one that the UK Government should side with the majority of people of Scotland and firmly tell her no?”