Theresa May has struggled to explain how her post-Brexit customs plan will work, during a difficult appearance before a Commons committee where one senior MP said the proposals had left her “really baffled”.

In tough exchanges at the liaison committee, which brings together the chairs of each of the subject-specific select committees, the prime minister eventually seemed to concede that elements of the plan were still to be decided.

Coming shortly after the former foreign secretary, Boris Johnson, labelled May’s customs idea “a fantastical, Heath Robinson customs arrangement”, the PM was pressed repeatedly on the issue by Yvette Cooper.

The Labour MP, who chairs the home affairs committee, asked how mutual trade in a future era of potentially different tariffs would work, noting that the Brexit white paper says Britain is “not proposing that the EU applies the UK’s tariffs and trade policy at its border for goods intended for the UK”.

This is a key contradiction for May’s “facilitated customs arrangement”, after she a accepted on Monday an amendment to the customs bill that said the UK could not collect duties on goods on behalf of the EU unless there was a reciprocal arrangement.

May said there was no disconnect, insisting the white paper allowed for reciprocity. She said it proposed a method under which any varying tariffs would be collected for goods arriving in the UK destined for the EU, and vice versa.

“The important thing here is there is reciprocity in the sums of money that would be paid,” she said.

However, under repeated questioning from Cooper, May struggled to explain how the system would actually operate.

“This is not a question of somebody physically handing cash over at the border,” the PM said, but added only that a “formula revenue agreement” would determine what payments were made and to whom.

Cooper asked where this would happen. May replied: “There will be a formula agreement with the the European Union in terms of the sums of money ... Importers will be under a requirement to ensure they have paid the correct tariffs.”

When she was then asked to whom the money would be paid, she responded: “What matters is what money comes to the United Kingdom.”

After more expressions of confusion from Cooper, May appeared to concede that many details had yet to be worked out.

Cooper said May’s responses had left her “really baffled”, adding: “We’ve still got this statement in the white paper which says that we’re not going to have the EU applying the UK’s tariffs and trade policies at the border, but you accepted an amendment, new clause 36 two days ago, which requires reciprocity.”

Cooper said such vagueness risked jeopardising public faith in May’s Brexit plans: “Everybody’s confused, and as a result nobody trusts what the government is doing.”

May responded: “I’m not sure what is baffling about it, exchanging sums of money that are relevant to both parties, but there we are.”