Ian Blackford said the UK’s commitment to “full alignment” with EU regulations as part of a deal to keep the Irish border open meant the government would eventually have to concede remaining within the European trading bloc.
It came as David Davis warned that the ‘divorce’ agreement struck last week, including a financial settlement with the EU of over £35 billion, would only apply if trade talks are successful.
The Brexit secretary said he was seeking a “Canada plus plus plus” deal that adds access to services to the CETA agreement signed off by Ottawa and Brussels last year.
Speaking on the Andrew Marr programme, Mr Blackford challenged Labour to support the SNP’s calls for continued membership of the single market to avoid “unparalleled” economic damage.
Shadow Brexit secretary Keir Starmer said Labour wanted the UK to “very, very close” to existing EU rules, including continued “easy movement” of European nationals to live and work in the UK, but stopped short of calling for ongoing single market membership which is opposed by senior members of Labour’s front bench.
UK ministers refused calls from the Scottish and Welsh Governments to be directly involved in the first phase of Brexit negotiations.
Talks seeking a comprehensive free trade agreement between the UK and EU are set to begin in February, with the cabinet yet to discuss what the “final state” relationship should be.
Mr Blackford said devolved administrations had to have a greater role in the second phase of negotiations to avoid the kind of disagreements over the Irish border that nearly blocked last week’s breakthrough.
“I would remind the Prime Minister that we’re talking about four nation states within the United Kingdom.
“We can see the difficulty she has gotten into over Ireland. What the Prime Minister should do is pull the First Ministers of Scotland and Wales into these negotiations.
“She’s also got to understand that the people in Scotland and in Northern Ireland voted to remain in the EU and we’re asking for her to respect the wishes of the Scottish people and the Scottish Government, who have made it clear that we should be staying in the single market and customs union.”
He added: “It’s about the living standards of people post-Brexit. What we have now is a situation where the UK has signed up to have full convergence with [the Republic of] Ireland and the rest of Europe.
“It’s the ‘how’ bit of that that’s important. What I’m saying to the Prime Minister and everyone else is that the single market and the customs union is the path to doing that.”
The SNP’s Westminster leader insisted that staying in the single market and customs union would be “consistent with the vote that took place in the UK last year."
He told the BBC: "What we want Labour to do is to get behind us and others that are arguing that we should stay in the single market and the customs union.
"If you look at the agreement that has come forward over the last few days about full alignment in order to deal with the Irish question, the simple answer to that is to stay within the single market and the customs union."
He added: "I think the fundamental point is that nobody voted in that referendum to become poorer and it's about that threat which is becoming clearer to jobs and prosperity."
"If we go into a hard Brexit without the protection of the single market and the customs union, there is an economic threat to this country which is unparalleled in recent times."
Meanwhile, Mr Davis appeared to contradict comments by Philip Hammond, who has said it was "inconceivable" that the UK would not pay its Brexit bill even if trade talks fail.
The Brexit secretary said the multi-billion pound financial settlement was "conditional on an outcome".
"No deal means that we won't be paying the money," he said.
Mr Davis said the chances of Britain leaving the EU without a trade deal and being forced back into World Trade Organisation (WTO) tariffs had now "dropped dramatically".
He insisted that agreeing to "full alignment" with the EU in standards and regulations that impacted on Northern Ireland was not the same as "non-divergence" which would have meant "cutting and pasting" rules from Brussels.
"This was a statement of intent more than anything else," Mr Davis said of last week's deal. "Much more a statement of intent than it was a legally enforceable thing."