Theresa May has refused to say whether her customs plan requires EU border staff to collect duties for the UK after Brexit, prompting an accusation that she is “not being straight”.

Under fierce questioning, the prime minister declined – four times – to explain how her “facilitated customs arrangement” will work, even as she seeks agreement in Brussels.

Asked repeatedly if payments would have to be collected at borders – something the EU is expected to reject – she would go no further than the need to agree a “tariff revenue formula”.

Several times, Ms May said that “what matters is what money comes to the United Kingdom”, eventually suggesting it was a matter for the negotiations.

At one point, a flustered prime minister referred mistakenly to a “future customs arrangement” and a “facilitated customs agreement”.

Yvette Cooper, the Labour chairwoman of the Commons home affairs committee, went on the attack, saying: “I’m really baffled as to what’s going to happen.”

She said: “Don’t you have a problem that you are not being straight about the language and about what it is you are actually proposing?

“So, everybody is confused and, as a result, no one trusts what the government is doing.”

People's Vote march – demanding vote on final Brexit deal Show all 30 1 /30 People's Vote march – demanding vote on final Brexit deal People's Vote march – demanding vote on final Brexit deal Mandatory Credit: Photo by Guy Bell/REX (9725259aq) Marching down Whitehall - People's March for a People's Vote on the final Brexit deal. Timed to coincide with the second anniversary of the 2016 referendum it is organised by anti Brexit, pro EU campaigners. People's March for a People's Vote, London, UK - 23 Jun 2018 Guy Bell/REX Rex People's Vote march – demanding vote on final Brexit deal Demonstrators carry banners and flags as they participate in the People's March demanding a People's Vote on the final Brexit deal, in central London on June 23, 2018, the second anniversary of the 2016 referendum. Tens of thousands of people demonstrated in London on Saturday calling for a second vote on Britain's departure from the European Union. / AFP PHOTO / Niklas HALLE'NNIKLAS HALLE'N/AFP/Getty Images NIKLAS HALLE'N AFP/Getty Images People's Vote march – demanding vote on final Brexit deal A young protestor shouts as she takes part in the People's Vote demonstration against Brexit Getty Images People's Vote march – demanding vote on final Brexit deal A woman holds a placard as she joins EU supporters, calling on the government to give Britons a vote on the final Brexit deal, participating in the 'People's Vote' march in central London, Britain June 23, 2018. REUTERS/Henry Nicholls HENRY NICHOLLS Reuters People's Vote march – demanding vote on final Brexit deal epa06833888 Pro-EU demonstrators take part in a People's March anti-Brexit rally in Parliament Square in London, Britain, 23 June 2018. Protesters are calling for a referendum on the final deal. The protest is taking place on the second anniversary of the Brexit referendum. EPA/ANDY RAIN ANDY RAIN EPA People's Vote march – demanding vote on final Brexit deal A protester's pro-EU t-shirt EPA People's Vote march – demanding vote on final Brexit deal epa06833892 A pro-EU demonstrator waves a European Flag during a People's March anti-Brexit rally in Parliament Square in London, Britain, 23 June 2018. Protesters are calling for a referendum on the final deal. The protest is taking place on the second anniversary of the Brexit referendum. EPA/ANDY RAIN ANDY RAIN EPA People's Vote march – demanding vote on final Brexit deal Demonstrators carry banners and flags as they participate in the People's March demanding a People's Vote on the final Brexit deal, in central London on June 23, 2018, the second anniversary of the 2016 referendum. 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Tens of thousands of people demonstrated in London on Saturday calling for a second vote on Britain's departure from the European Union. / AFP PHOTO / Niklas HALLE'NNIKLAS HALLE'N/AFP/Getty Images NIKLAS HALLE'N AFP/Getty People's Vote march – demanding vote on final Brexit deal epa06833964 A young pro-EU demonstrator takes part in a People's March anti-Brexit rally in Parliament Square in London, Britain, 23 June 2018. Protesters are calling for a referendum on the final deal. The protest is taking place on the second anniversary of the Brexit referendum. EPA/ANDY RAIN ANDY RAIN EPA People's Vote march – demanding vote on final Brexit deal Gina Miller and Caroline Lucas EPA People's Vote march – demanding vote on final Brexit deal epa06834044 Tens of thousands of people march through London during a People's March anti-Brexit demonstration, in London, Britain, 23 June 2018. Protesters are calling for a referendum on the final deal. The protest is taking place on the second anniversary of the Brexit referendum. EPA/ANDY RAIN ANDY RAIN EPA People's Vote march – demanding vote on final Brexit deal epa06833264 Thousands of people march through London during a People's March anti Brexit demonstration in London, Britain, 23 June 2018. Protesters are calling for a referendum on the final deal. The protest is taking place on the second anniversary of the Brexit referendum. EPA/ANDY RAIN ANDY RAIN EPA People's Vote march – demanding vote on final Brexit deal Tens of thousands of people march through London EPA People's Vote march – demanding vote on final Brexit deal epa06833265 Thousands of people march through London during a People's March anti Brexit demonstration in London, Britain, 23 June 2018. Protesters are calling for a referendum on the final deal. The protest is taking place on the second anniversary of the Brexit referendum. EPA/ANDY RAIN ANDY RAIN EPA People's Vote march – demanding vote on final Brexit deal Demonstrators at the People's Vote March Getty People's Vote march – demanding vote on final Brexit deal 'Two months too young to decide on my future' REUTERS People's Vote march – demanding vote on final Brexit deal Crowds taking part in the People's Vote march for a second EU referendum at Trafalgar Square in central London. PRESS ASSOCIATION Photo. Picture date: Saturday June 23, 2018. See PA story POLITICS Brexit. 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PRESS ASSOCIATION Photo. Picture date: Saturday June 23, 2018. See PA story POLITICS Brexit. Photo credit should read: John Stillwell/PA Wire John Stillwell PA People's Vote march – demanding vote on final Brexit deal Crowds gather on Pall Mall PA People's Vote march – demanding vote on final Brexit deal A man resembling Britain's Foreign Secretary Boris Johnson, joins EU supporters Reuters People's Vote march – demanding vote on final Brexit deal EU supporters, calling on the government to give Britons a vote on the final Brexit deal, participate in the 'People's Vote' march in central London, Britain June 23, 2018. 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But Ms May insisted: “I have been very straight about the language” – arguing it had all been set out in the white paper on her Chequers plan.

On the suggestion that her proposals were “baffling”, the prime minister said: “I’m not sure what is baffling about us exchanging sums of money that are relevant to both parties.”

During an exchange lasting ten minutes, Ms May did make clear that the plan would not involve “someone physically handing cash over at the border”.

Giving evidence to the heads of all Commons committees, Ms May also admitted that only the “majority” of the plan would be ready for December 2020, the end of her proposed transition period.

And, asked to identify where else in the world such a complex system already exists, she replied: “It doesn’t – it’s a novel idea.”

The prime minister also ducked a question about whether a no-deal Brexit would trigger a hard border in Ireland, saying: “There isn't a sort of simple answer to that.”

The customs plan, unveiled at Chequers a fortnight ago, promises tracking technology to allow the UK to collect, and pass on, the tariffs on goods destined for the EU.

However, after she caved in to demands from the hardline European Research Group (ERG), that will now be “illegal” unless the EU also collects duties for the UK.

Ms Cooper said the issue of collection at EU borders would arise if the UK ended up with higher tariffs than the EU for goods imported from some countries.

Earlier, Ms May said only the “majority” of the plan would be ready for the end of the 21-month transition she is seeking, after the UK leaves the EU next March.

“There is a question as to the speed with which the repayment mechanism would be in place,” she admitted.

“So far, the suggestion is that could take longer to be put into place. That has yet to be finally determined.”

Sarah Wollaston, the Conservative chairwoman of the health committee, urged her to be “transparent” with the public about what they needed to do to prepare for a no deal.

Her committee had heard evidence that people with long-term health conditions would be uninsurable in those circumstances, she warned.