She told LBC radio: “I don’t answer hypothetical questions.”
Instead she defended her decision to vote remain at the time of the vote, but signalled things have changed.
Seizing on the opportunity during the House of Commons debate today, SNP’s leader in Westminster, Ian Blackford, said: “If there was another EU referendum now I know how I would vote to remain. Why hasn’t the Prime Minister been straightforward about how she would vote?”
Mrs May fired back: “Let’s be clear – there is no second referendum.
“The people of the United Kingdom voted and we will be leaving the EU in March 2019.”
Parliament erupted with cheers and jeers with one MP shouting: “You might want one, we don’t.”
Mr Blackford tried to continue the attack, adding: “The Prime Minister can’t answer a simple question because she’s hamstrung by the parliamentary majority and a divided party of right wing Brexiteers.”
He went on to say the Scottish economy was at risk of losing 80,000 jobs and £2,000 per person if Britain left the single market and customs union.
But Mrs May said: “Now is the time for the SNP leadership to recognise that to save jobs in Scotland they need Scotland to remain part of the UK.
Mrs May was urged to stop NHS cuts to improve mental health funding.
The PM said the Government is putting more money into mental health and more NHS patients have access, however she said more needs to be done.
She said teachers in schools are also being trained.
Onto trade – Mrs May was asked if she would issue a white paper on the future of trade in services.
The PM said during the Brexit implementation period they will continue to concentrate on trade.