The Prime Minister is poised to begin official talks with the European Union once legislation allowing her to do so has been passed.
She has vowed to opt for a clean-break from the bloc, which includes forging a new trade deal outside of the single market.
Iain Dale and Alex Salmond clashed during a heated row on LBC
Why won’t you respect the will of the British people and vote to trigger Article 50?
The SNP previously tried to reject the Government’s Brexit Bill, which will once again be voted on by MPs in the Commons next week.
Mr Salmond’s party position came under attack from LBC host Iain Dale, who grilled the Europhile during his regular phone-in on Wednesday.
Dale reminded him that despite 62 per cent of Scots voting to Remain, the majority of Britain voted to leave the EU.
The SNP MP said Theresa May had "no mandate" to remove Britain from the EU's single market
“Why won’t you respect the will of the British people and vote to trigger Article 50?” Dale questioned.
To which the SNP MP retorted: “Because I don’t believe the prime minister has the mandate to take the country out of the single market.
Get Quotes on Home Insurance
“Taking us out of the single market was not on the ballot paper.”
Nicola Sturgeon's most memorable quotes Wed, March 8, 2017 Getty Images 1 of 10
'True gender equality in Scotland – and elsewhere – is still some way off'
As the pair became embroiled in a heated row, Dale fired back: “The single market is part of the European Union, it was set up by the European Union!
“If we stay in the single market we’ll have to accept freedom of movement, it was quite clear in the EU referendum what the British people wanted to do.”
To which Mr Salmond used the rhetoric: “We had a huge majority in Scotland to Remain, it was a narrow majority to Leave in England.”
The point was quickly slapped down by Dale who, becoming increasingly frustrated, argued: “Let me remind you you’re still members of the UK.”
On Wednesday, Lords added a second amendment to the Government’s legislation to begin Brexit talks.
Unelected peers voted in favour of demands that Parliament is given a “meaningful” vote on the prime minister’s final deal with the EU.
Last week they also insisted the rights of EU nationals living in the UK are protected before talks begin.
The legislation returns to the Commons next week, where MPs will decide whether to bow down the upper chamber.