The British Labour party member John Mcdonnell exposed clearly what his party intends to do regarding the Brexit.
During an interview with Robert Peston, Mcdonnell (who is currently the shadow chancellor) said that under the current circumstances the Labour Party would "certainly remain." This was making a reference to the prevailing uncertainty regarding the viability of a Brexit with a deal, as May's deal has been rejected multiple times in the parliament and the European Union leadership is not willing to renegotiate it.
"We’ll see if Boris Johnson comes back with some sort of deal, we’ll look at that, just as we did last time, but at the moment, I can’t see him stitching up a deal either to Labour or to quiet a bit of his own side as well,” he explained when asked to be more straightforward, “It looks as though we’ll be in a straight situation between no deal and remain,” he added.
This suggests that the Labour party may be willing to support Boris Johnson if he's actually successful at producing an improved deal that could be accepted by the EU leadership in Brussels. This would be a significative change from their former Brexit stance since they are currently pushing for a new referendum and favoring remaining in the European Union. However, according to his statements, Labour's former position is based on a situation where leaving without a deal is the alternative.
This is somewhat contradictory when it comes to Jeremy Corbyn's position, who clearly favors a referendum (whether there is or isn't a deal).
"Whoever becomes the new Prime Minister should have the confidence to put their deal, or no-deal, back to the people in a public vote. In those circumstances, I want to make it clear that Labour would campaign for Remain against either no-deal or a Tory deal that does not protect the economy and jobs," said Corbyn two weeks ago, statements that were reinforced by Corbyn's spokesman this week.