Shadow foreign secretary Emily Thornberry has hinted Labour could back remaining in a European customs union after Brexit.
Her comments came as former shadow home secretary Yvette Cooper called on the party to support staying in the customs union after any Brexit transition period.
Ms Thornberry said that "we've looked at it and we cannot see a way forward when it comes to Northern Ireland or to tariff free trade across Europe without us being in some form of customs union, that probably looks very much like the customs union that there is at the moment".
Ms Thornberry insisted Labour members did have a voice on Brexit policy.
She told ITV's Peston on Sunday: "We've got the national policy forum going on at the moment... so there will be a debate."
Asked about whether the majority of Labour members would like the party to sign up to a policy of continued membership of the single market and the customs union, and if the party was on the way to doing so, she said: "What we do is we accept the result of the referendum, we have to leave the European Union, if we're leaving the EU then we have to negotiate an ongoing relationship with the EU.
"We want to have, we've looked at it and we cannot see a way forward when it comes to Northern Ireland or to tariff free trade across Europe without us being in some form of customs union that probably looks very much like the customs union that there is at the moment, and that's our position on that.
"As for the single market, you know and I know that it's very difficult for us to remain in the single market as it currently is because nobody can pretend that the referendum didn't include a debate on immigration and we want to have fair rules and managed migration when it comes to immigration so we need to negotiate something."
Ms Thornberry said any deal needed to look after jobs and the economy first and foremost, adding: "Nobody voted to be poorer and nobody voted to lose their job."
Senior Labour MP Yvette Cooper said the party should back remaining in the customs union.
"The Labour party said that we should be in both the single market and the customs union during the transition, I think that's right but I would go further to what happens after the transition because for manufacturing areas, if you care about manufacturing and distribution across this country, Yorkshire, the North and the Midlands, actually we need that customs union," she told Sky News.
"I understand that the Shadow Cabinet I think are meeting tomorrow, I hope this is exactly what they'll look at, I hope they will say 'look we need a customs union' and I think there is really strong support for this across Parliament as well."
Commenting on Foreign Secretary Boris Johnson's Brexit intervention this week, leader of the Scottish Conservatives Ruth Davidson told ITV's Peston on Sunday that he "walks a pretty fine line in that that speech actually".
Ms Davidson said she wanted to see a comprehensive free trade agreement with the EU to trade with and operate within, "to the maximum possible extent the single market", but added that the UK "should be able to get trade deals with other countries too".
Falling out on WTO rules, she added, would not be something that would be in the benefit of the country, but added: "I don't think anybody's working to a no deal scenario."