MPs will debate EU customs union legislation today.
The debate in the Commons comes after Theresa May suffered a defeat on the issue on the House of Lords, but as a backbench debate, it is not binding.
The votes that count will come next month – the EU (Withdrawal) Bill is currently being reviewed in the House of Lords and is due to return to Commons in May.
Today’s debate was proposed by Labour MPs Yvette Cooper, Hilary Benn, Meg Hillier, Rachel Reeves and Mary Creagh, Conservatives Nicky Morgan, Sarah Wollaston, Dominic Grieve and Bob Neill, the SNP’s Angus MacNeil and Pete Wishart, and Lib Dem Norman Lamb.
Public Accounts Committee chair Meg Hillier told Sky News: “I chair a cross-party select committee made up of four parties who all voted different ways on Brexit. Some voted for, some voted against.
“But we are united in our concern about how ill prepared the Government is for Brexit and customs and the border.”
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 UK economy £24 billion by 2033.
Shadow Brexit Secretary Sir Keir Starmer said: "Over the past few weeks it has become abundantly clear that Theresa May is unwilling and unable to put the country's interests first during the Brexit negotiations.
"She has wasted 12 weeks of the Brexit negotiations delaying a Commons vote on the UK negotiating a customs union with the EU for fear of a defeat.”
But Brexit minister Suella Braverman said Labour's support for a customs union "would leave the UK shackled to Brussels", taking rules set by the EU and unable to strike trade deals.
Labour leader Jeremy Corbyn has backed a customs union but only if the UK had a say in future EU trade deals.
Mrs Braverman said: "The supposed safeguards that Corbyn talks about are impossible to achieve and will get laughed out of town."
She said Labour was "more interested in frustrating the process and playing politics than they are in delivering a successful Brexit".
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".