Following the defeat of Theresa May’s Brexit deal, Sir Keir said the choice lay between instructing the Government to negotiate a close economic relationship with the EU based on a customs union, and a further public vote.
Speaking at the Fabian Society’s new year conference in London, he said that with time running out before before Brexit day on March 29, it now appeared “inevitable” the Government would have to apply for an extension to the Article 50 withdrawal process.
He drew the loudest cheer, however, when he said Labour stood by the commitment made at the party conference last year in Liverpool that if it was unable to force a general election all options must remain on the table - including another referendum.
“That is a very important commitment. It’s a commitment to you, our members and our movement. And it is one we will keep,” he said.
“As I set out in Liverpool, a public vote has to be an option for Labour. After all, deeply embedded in our values are internationalism, collaboration and cooperation with our European partners.”
Sir Keir again made clear that he believed that in the event of a second referendum, the option of remaining in the EU must be on the ballot paper.
“I don’t think it is any secret I firmly believe there should be a Remain option - and there has to be a genuine Leave option,” he said.
He said that with the raft of legislation that still needed to get through Parliament before Brexit, it was difficult to see how an extension to Article 50 could be avoided.
“It seems inevitable to me that the Government will have to apply for an extension of Article 50,” he said.
“So, it’s time for us to inject some honesty into this debate, and to identify the credible solutions that remain.
“In the coming weeks Parliament will have the chance to take control. That starts by being open about the dilemmas we face, and the credible choices that are still available.”
Earlier, Sir John Major called for a free vote for MPs to break the deadlock in Parliament over the way forward on Brexit.
The former prime minister - whose time in office was beset by divisions over Europe - said the Commons had “comprehensively” killed Mrs May’s plan.
He said there now needed to be a series of “indicative” votes to establish which, if any, the various alternative proposals could command the support of a majority of MPs.
As an “act of statesmanship”, he said all the party leaders should give their MPs a free vote to allow an “honest representation” of opinion in the House.
“It is the only way to get an absolutely honest answer from Members of Parliament and if it is a free vote it removes the danger of resignations from Government or the opposition frontbench because they disagree with their leader’s policy,” he told the BBC Radio 4 Today programme.
“It is a unique way of doing it but I think it is justified.”