Mr Corbyn also said today that there would "have to be a customs union with the EU obviously" but again insisted that Britain can not be a part of the EU's Single Market without being a member of the EU.
He added: "We've had a Referendum and we lost and you won, I accept that" but he said the public was becoming more anxious about the issue.
Labour MP Chuka Umunna told Sky News shortly after Corbyn's comment: "In terms of the notion you have to be in the European Union to be part of the single market, that is not correct".
Mr Corbyn said that he was not calling for a second referendum.
"The Single Market is dependent of membership of the European Union".
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"Noway, Lichtenstein and Iceland fully participate in the single market but they are not members of the EU".
He said: "Once again the very top of Labour, this time Jeremy Corbyn and Emily Thornberry, have failed to rule out a second referendum".
Meanwhile, shadow foreign secretary Emily Thornberry said that if 90% of people were calling for another vote, it would present a challenge "for all of us who are democrats".
"At the moment... We proceed in good faith".
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And she admitted that it was a "deep balancing act" to please both Labour voters who backed Brexit, and Labour members who want to stay in the EU. However the survey said only 18% of Tory voters want a second poll and 79% were against.
Labour has said it wants the "closest possible ties" with European Union markets after Brexit.
Sir Keir said he wanted the same trade outcomes as backbench critics calling for the party to campaign to stay in the single market and customs union.
The party leader reiterated his call for MPs to have a "meaningful vote" on the final Brexit deal.
Labour has also been urged to join a cross-party bid to keep the United Kingdom in the single market and customs union after Brexit.
Scottish First Minister Nicola Sturgeon insisted that staying in the Market and Customs Union would be the "least damaging" option post-Brexit - and called on the Labour leader to get behind it. The SNP, Liberal Democrats, Plaid Cymru and Greens have joined forces to back an amendment to the EU (Withdrawal) Bill when it returns to the Commons this week.
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