Responding to Rudd's comments, Shadow Brexit Secretary Keir Starmer said: "Amber Rudd appears to have let slip that discussions around the cabinet table about negotiating a customs union with the EU have not in fact concluded".
"We are leaving the customs union and won't be joining a customs union", he said, repeating that such an agreement would constrain Britain's ability to sign its own trade deals.
The unelected Lord's last week voted on an amendment that throws into doubt May's plans to leave the EU's customs union, setting the stage for a fresh round of parliamentary battles over her strategy.
Lawmakers will this week hold a nonbinding vote on the future of Britain's trade after Brexit.
"It's no good pretending to be in a parallel universe in which all of things we might want to be true just simply aren't".
But political commentators say a defeat could influence May's future attitude after months of insisting that Britain would be leaving both the customs union and the European single market.
That has sparked suggestions that Mrs May could be forced to remain in the customs' union.
Speculation that Theresa May could accept a customs union has mounted since her Lords defeat last week, prompting reports that senior Brexiteers including Boris Johnson would reject any dilution of her "red line" on withdrawal.
Thursday's Commons debate is not binding on the Government and was not attended by many pro-Brexit MPs, with Tories not whipped to take part in the vote.
Since losing her Conservatives' majority in parliament in an ill-judged election a year ago, the prime minister is dependent on a small Northern Irish party which opposes a backstop agreement with the European Union that would see the province become more aligned with the bloc than with mainland Britain. "Such a small proportion of total European Union trade relates to the Republic of Ireland, yet the Irish Government have got into a position where it is their country that the European Union is listening to", she said.
House of Commons library analysis commissioned by Labour indicated the decision to rule out a new customs union with the European Union could cost the United Kingdom economy £24bn by 2033. But it would be possible to establish a U.K. -EU dialog on trade and the European Union would take a pragmatic approach to such a setup. May's government is already showing "a steady shift to a soft Brexit", she wrote in the presentation.
"It seems rather perverse that at a time when we want to increase free trade, we're going to put up a whole load of barriers to stop access in that best free trade area that is existing in the world", said Conservative MP Anna Soubry. "The answer is categorically yes".