In a speech to the Fabian Society's annual conference in London on Saturday, Streeting will say: "On the UK's future relationship with the European Union - the single biggest issue facing our country in a generation - we find ourselves in the bad position where it is the Labour party that now stands as the single biggest barrier to the UK's membership of the single market and customs union".
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.
However, Mr Corbyn sidestepped the question of whether Labour could support a new referendum in the future.
The Labour leader said his party were not in favour of another vote at the moment - but wouldn't be drawn on whether he would stick to it in future.
Speaking on Peston on Sunday, he continued: "The single market is dependent on membership of the European Union".
"Noway, Lichtenstein and Iceland fully participate in the single market but they are not members of the EU".
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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". "We are leaving the European Union".
In an interview with The Observer today, the former Ukip leader said he was anxious Brexiteers could "lose the historic victory" they won in 2016 as "The Remain side are making all the running".
Alastair Campbell believes there will be a "fresh referendum" and/or a general election but said that he now believed "Brexit will happen and it will be a disaster". However the survey said only 18% of Tory voters want a second poll and 79% were against.
The Labour leader cited European Union state aid rules as another reason why he wanted to be outside the single market, despite conceding that Brussels would not stand in the way of Labour implementing its manifesto.
He said if the Labour leadership committed to staying in the trading arrangement it would be a "game-changing moment" in British politics as it would command a majority of cross-party MPs.
Mr Sturgeon lashed out at the Labour leader on Twitter, arguing he was misleading people by arguing Brexit meant leaving the single market.
The comments came after some Labour figures called for the party to change tack and campaign to remain in the single market and customs union after withdrawal.
This is the goal of an amendment to the EU (Withdrawal) Bill being backed by the SNP, Liberal Democrats, Plaid Cymru and Greens which returns to the Commons this week.