"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.
Some British media has suggested that this vote may become a confidence vote: meaning that if the government loses the vote, it has 14 days to win a confidence vote.
"I'm not voting to make my constituents poorer and to prevent businesses being able to trade as quickly and smoothly with their biggest market", she wrote on Twitter after the motion was published.
Pro-European MPs say there is growing support for a change of tack, and many took part in a House of Commons debate Thursday backing a 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.
Prime Minister Theresa May wants to pull Britain outside the EU's customs union area but avoid erecting a "hard border" between Ireland and Northern Ireland. This is not just about free trade agreements, this is about frictionless trade, this is about jobs and investment and supply chains.
The ministers believe that the so-called customs partnership put forward by May is unworkable and is encouraging Brussels to press for Britain to stay in a customs union after Brexit.
Brexit supporters say remaining in any European Union grouping will force Britain into becoming a "vassal state".
The Conservative government has repeatedly ruled out continued membership of a customs union after Britain leaves the European Union in March 2019, arguing that it would limit their ability to strike trade deals with other countries.
Her comments provoked anger among Leave-supporting Tories who accused her of trying to undermine the Prime Minister.
Asked whether it was more or less likely, in the current climate, that Britain would stay in the customs union, Ms Rudd said: "I'm not going to be drawn on that".
The motion being debated on Thursday calls on the Government to include as an objective in negotiations with the EU "the establishment of an effective customs union between the two territories".
The biggest outstanding issue is how to avoid a hard border in Ireland if the United Kingdom leaves the single market and customs union, as the United Kingdom government now intends.
Lord Pannick, who won the Article 50 case against the Government, said that to exclude a number of important European Union rights from domestic law would lead to a lack of certainty and continuity, providing a "recipe for confusion" after Brexit.
"In every other aspect we are effectively remaining in the European Union as a vassal state".
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