Ian Blackford told Scotland on Sunday that momentum towards a soft Brexit was building and MPs could keep the UK in the trading bloc if Tory rebels held their nerve.
With Labour now backing single market and customs union membership during a post-Brexit transition phase of up to four years, debate this week on key Brexit legislation would allow an “informed debate” to win “hearts and minds” inside and outside parliament, he said.
Ahead of the second reading of the European Union (Withdrawal) Bill on Thursday, the SNP’s Westminster leader said enough Tory MPs had doubts about the government’s plan to leave the single market to force a change.
“There are others in the party who are concerned, and they need to have the courage of their convictions,” Blackford said.
“There is a very compelling case to be made that yes, we accept the position of the UK to leave the EU, but that doesn’t then mean you have to leave the single market and the customs union.
“If we can start to have an informed debate about that, then I do believe we can win hearts and minds.
It would take just seven Conservative MPs to switch sides to force a Commons defeat, as the minority government relies on the votes of 10 DUP MPs to pass legislation.
However, at least half a dozen Labour MPs have previously voted with the government on Brexit, suggesting at least a dozen Tories would have to rebel in order to amend the Withdrawal Bill.
This week Conservative MP Anna Soubry co-authored a cross-party report warning of the dangers of pulling out of the mechanisms that allow EU member states to trade freely. Others including former ministers Maria Miller and Kenneth Clarke also favour a soft Brexit.
Shadow Brexit secretary Keir Starmer opened the door to the UK staying in the single market by reversing Labour’s position and arguing that the UK should stay in the single market and customs union for “as long as necessary” after leaving the EU in March 2019, but hinted that Labour could adopt that position permanently.
Blackford said: “Parliamentary arithmetic is leading us into a situation where like-minded people can seek to protect the interests of people of Scotland as well as the people of the rest of the UK.
“Whilst no-one would seek to nay-say the vote that was taken to withdraw from the EU, the point I would make is that no-one was asked specifically if the UK should remove itself from the single market and the customs union.”
Concerns have also been raised about sweeping powers in the Withdrawal Bill that allow ministers to amend the law without going before parliament for as long as two years.
Critics fear so-called “Henry VIII” powers could be used to slash away at workplace protections and business regulations currently enforced within the EU.
The SNP is trying to stop EU regulations in areas such as agriculture, fisheries and the environment that are currently exercised by the Scottish Government being ring-fenced by Westminster.
UK ministers say some of those powers will then be devolved, but the Scottish and Welsh administrations have condemned the plan as a “power grab”.
“The most important thing is that there shouldn’t be any detriment to the devolved administrations,” said Blackford, who called for talks between all three governments on post-Brexit powers.