This comes after 83 party members voted for an amendment to the EU Withdrawal Bill that would keep the country in the European Economic Area.
Radio Sputnik discussed the issue with Martin Smith, a professor at the Department of Politics at the University of York.
Sputnik: What does the proposed referendum tell us about the state of affairs in the Labour Party?
Martin Smith: I think that the problem's that the Labour, like the Conservatives, is that the party is split on the issue. The difference of the Conservative Party is that Labour's split is really between the leadership and the rest of the MPs and many of the members. Whilst Jeremy Corbyn has been for a long time been a skeptic about the European Union, many Labour MPs are strongly supportive of the European Union. And even if they recognize that Britain now has to leave, they want to remain in the single market and the customs union.
Sputnik: Do you think more MPs will break ranks?
Martin Smith: Whether they break ranks depends on the line that Jeremy Corbyn takes. I think you have seen his position shift, actually, since the referendum, where at one point he was very opposed to staying in the single market or the customs union and I think the Labor's position on that has softened quite a lot. I think whether the party stays together, depends a bit on what position Jeremy Corbyn takes in a few weeks' time.
Sputnik: How can this ongoing struggle affect the party's position on Brexit and do you expect any changes could be made?
Martin Smith: I think that, actually, that Labour's position, as I said, is changing. Part of the issue is that Labour will want to try to exploit divisions within the Conservative Party if they can, as a party, agree on a line on Britain post-Brexit that keeps the party together. That puts him in a stronger position to create problems for the Conservative Party. So, I think there's a lot of pressure on Labour to shift to a softer position on Brexit and I think a lot of their voters want a softer position and a large number of their MPs. So I think we will start to see Labour's position shift.
Sputnik: And what would this all mean for Mr. Corbyn given that he is under a barrage of criticism himself?
Sputnik: Could we be talking about a looming full-blown crisis for the Labour and, if yes, what scenarios and ways out do you envision?
Martin Smith: To be honest I don't think it will lead to a full-blown crisis. I think the party leadership is quite aware of the views of MPs and the members. And I think it's quite aware of the need to exploit Conservative difficulties. So I think the pressure on Corbyn and the leadership will be to try to get to a position that has the support of the MPs and the members. So I don't think actually he is going to get to a crisis. I think there's enough support for a soft Brexit within the Labour Party to pull Corbyn back into that position.
Sputnik: And what about the Tories? Do you think they would be able to take advantage of the situation?
Martin Smith: Of course the Conservatives have real problems in relation to Europe and the party's fundamentally split. I think they might see this as a bit of a light relief for them but actually, it doesn't resolve the problems they even have at cabinet level in terms of what Britain should do post-Brexit. So I think this is pretty much a side issue for the Conservatives because they've got such fundamental problems on this issue themselves.
The views and opinions expressed by Martin Smith are those of the speaker and do not necessarily reflect those of Sputnik.