SCOTLAND could remain a member of the EU single market with its own immigration regime while the rest of the UK departed in a hard Brexit, Nicola Sturgeon said yesterday.

The First Minister acknowledged it would be “challenging”, but said the Scottish Government would publish proposals on securing a special deal for Scotland in the coming weeks.

It followed Ms Sturgeon saying on Saturday that unless Theresa May shielded Scotland from a hard Brexit involving loss of single market membership, she would hold a second referendum.

Read more: Scotland's only Labour MP hasn't talked to Jeremy Corbyn in four months

A draft referendum bill is due out this week for public consultation.

In a round of TV appearances, the First Minister told the BBC’s Andrew Marr show: "We are going to put forward proposals, that we would hope that the UK Government would be prepared to listen to, that would allow Scotland to preserve its place in the single market and preserve aspects of its relationship with the EU."

However, she later suggested a deal was improbable, telling ITV’s Peston on Sunday she believed another independence referendum was “highly likely” before 2020, and that she had grown more convinced of it in the four months since Scots voted 62-38 to Remain.

Ms Sturgeon also accused Mrs May of “not fully honouring” promises to develop a UK-wide position on Brexit, criticised her for holding "secret" Brexit negotiations, and said it was “unacceptable” that she had not shared her position with the public or parliament.

Read more: Scotland's only Labour MP hasn't talked to Jeremy Corbyn in four months

SNP Westminster leader Angus Robertson told BBC Sunday Politics Scotland that if the UK government offered an acceptable deal on Brexit, the threat of a second independence referendum would be lifted.

He said: “If the UK delivers on the priorities the Scottish Government is going to be setting out in the next week, that is going to be the focus of our continuing and renewed relationship in a European context. If the Scottish Government is satisfied, then I don’t see how the Scottish Government would pursue a further Scottish independence referendum."

However he said London did not seem to have taken the issue seriously so far, and it was right to consult on the referendum bill "just in case the UK government does not deliver”.

The SNP later confirmed Mr Robertson’s comments referred only to a referendum linked to Brexit, and the party remained fully committed to independence.

If Scotland were in a single market based on free movement of people and the rest of the UK was not, it would means different immigration regimes across the border.

However former First Minister Alex Salmond told Pienaar’s Politics on BBC Radio 5 that did not necessarily mean a “hard border” with controlled entry points.

Read more: Scotland's only Labour MP hasn't talked to Jeremy Corbyn in four months

He said there would be no need for a hard border if the UK Government used a Green Card system for workers to control immigration at the point of employment.

He said Ms Sturgeon’s “red lines” in any Brexit deal would be membership of the single market, not merely access to it, and protecting the rights of EU citizens in Scotland and Scottish workers.

Scottish Secretary David Mundell said it was “difficult” to see how the SNP’s single market plan could be achieved, but he would listen to any proposals that came forward.

“I’m willing to look at any proposal that takes forward Scotland’s interests,” he said.

Asked on the BBC Sunday Politics show if Westminster might block a second referendum, by denying Holyrood the requisite powers, he said: “Of course then could be another referendum, but we want to argue that there shouldn’t be. We believe that the decision has been made.”

Labour’s only Scottish MP, Ian Murray, said he suspected the SNP’s demands on Brexit would include something “undeliverable in order to keep independence on the table”.