Ian Murray voiced concerns that although the party’s position was now to back a People’s Vote, some prominent Labour frontbenchers may be “trying to row back on that”.
He insisted Labour must now “step up” and “enthusiastically” support the amendment being proposed by Labour MPs Peter Kyle and Phil Wilson - which would allow Theresa May’s Brexit deal to pass the Commons, but make it subject to a public vote, in which people could opt to remain in the European Union.
Mr Murray, who has been a prominent campaigner for a second Brexit referendum, spoke out on the issue at a fringe event at the Scottish Labour conference in Dundee.
He stated: “Now it is time to step up. We are 480 hours away (from Brexit) and if the Labour Party, the opposition, doesn’t step up next week the Kyle/Wilson amendment will either not come forward or it won’t win and we will end up in a situation with no-deal, no no-deal, and no extension.”
The Edinburgh South MP said it was possible next week’s votes in the House of Commons could see MPs again reject Theresa May’s Brexit deal - but also not back the amendments that would rule out a no-deal Brexit and extend the Article 50 timetable.
“The Prime Minister could be sitting on Friday with her deal down, no extension of article 50, and parliament not wanting a no-deal - and where on earth does that leave us?” he asked.
Mr Murray, who was the only Labour MP in Scotland between 2015 and 2017, continued: “My big criticism is yes, the Labour Party has now got into the right position but now it is time to step up.”
He added: “The problem with the Kyle/Wilson amendment is this: It will only pass if the Labour front bench enthusiastically support it, whip it. And then we win it.
“People are saying it looks as though the Labour frontbench are going to back it, are they going to whip it? Are they going to sack shadow ministers and shadow cabinet members, or threaten to sack them, if they don’t vote for it?”
He insisted: “We need the leadership of the party to enthusiastically back this, to make sure the party enthusiastically backs it.
“Of course there is going to be some people unhappy and some rebels in that, but unless you say to people: ‘This the 11th hour, the division bell is going to ring, you will go down that lobby or you will hand in your resignation’, we will not get the numbers. It’s as simple and straightforward as that.”