Leaving the custom union would likewise mean required traditions checks for each lorry between the United Kingdom and EU until the point that an organized commerce is hit with Brussels, conceivably causing major deferrals.
The vote is non-binding and May has made no pledge to resign over it, but the pressure will be ratcheted up should she lose.
The vote can be overturned by the lower house, the House of Commons, but underscores the deep divisions over Brexit across parliament and could encourage lawmakers hoping to derail May's plans to forge a new relationship with the EU.
Right-wing Brexiteers want May to make the debate a "back me or sack me" issue in order to persuade her own MPs from voting against her.
"We wanted to take control of our trade and how can you take control if you are in the customs union or a form of customs union whereby we follow the EU's rules in absolutely everything".
"I think the free trade agreement".
The PM and her Cabinet have over and over guaranteed that Britain will leave the EU Customs Union and not join any comparable game plan after Brexit.
Lawmakers will this week hold a nonbinding vote on the future of Britain's trade after Brexit.More news: Atletico's Simeone: Unlikely Costa plays 1st leg vs
With few pro-Brexit MPs attending the debate, the motion was approved without a vote, prompting Labour's Chris Leslie to suggest it "was now the default consensus view of this House" and said the government should respond.
May says Britain must leave the EU customs union, which sets external tariffs for goods imported into the bloc, so that it can independently negotiate trade deals with other countries. "If they did do that, I think the European Union could be quite responsive".
Supporters believe a new customs union is the only way to resolve the Irish border issue, dismissing the government's proposals for a technological solution.
"The government is absolutely clear and without ambiguity that we will be leaving the customs union and won't be joining a customs union", he told reporters.
Within an hour, amid a growing Twitterstorm in Westminster, Rudd used Twitter to clarify her comments.
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.
"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.
She said Labour was "more interested in frustrating the process and playing politics than they are in delivering a successful Brexit".