A leaked draft legal analysis produced for the European scrutiny committee by in-house lawyers warns that the UK will face “a practical barrier” to striking a trade deal with the US or other non-EU countries if the country falls into the backstop customs arrangements.

The remarks, contained within a draft paper that leaked on Monday morning, emerged hours before the attorney general, Geoffrey Cox, was scheduled to brief the Commons about his advice on the Brexit deal negotiated by May.

The 27-page document, dated 26 November, says the UK would conform to EU customs rules if it entered the backstop, and adds that this “would be a practical barrier to the UK entering separate trade agreements on goods with third countries”.

The Northern Ireland backstop has become the most controversial part of the legally binding withdrawal agreement struck by May with the European Union, because it ties the UK to EU rules in order to maintain an open border in Ireland if no free trade agreement has been signed.

Last week, Donald Trump unexpectedly declared he believed that Brexit deal would be “a great deal for the EU” and that the UK “may not be able to trade with us” as a result.

However, during the G20 summit over the weekend, May said the US president was wrong. She said: “I’m very happy to tell President Trump and others that we will have an independent trade policy, we will be able to do trade deals.”

Quick guide Brexit and backstops: an explainer Show Hide A backstop is required to ensure there is no hard border in Ireland if a comprehensive free trade deal cannot be signed before the end of 2020. Theresa May has proposed to the EU that the whole of the UK would remain in the customs union after Brexit, but Brussels has said it needs more time to evaluate the proposal. As a result, the EU insists on having its own backstop - the backstop to the backstop - which would mean Northern Ireland would remain in the single market and customs union in the absence of a free trade deal, prompting fierce objections from Conservative hard Brexiters and the DUP, which props up her government. That prompted May to propose a country-wide alternative in which the whole of the UK would remain in parts of the customs union after Brexit. “The EU still requires a ‘backstop to the backstop’ – effectively an insurance policy for the insurance policy. And they want this to be the Northern Ireland-only solution that they had previously proposed,” May told MPs. Raising the stakes, the prime minister said the EU’s insistence amounted to a threat to the constitution of the UK: “We have been clear that we cannot agree to anything that threatens the integrity of our United Kingdom,” she added.

Cox is expected to be questioned intensely by MPs as to what his legal advice says about the backstop, amid criticism that the UK could not exit the customs arrangement without the permission of the EU.

He will speak to MPs on Monday afternoon, at a time when then government is at risk of being declared in contempt of parliament in a row over the publication of official legal advice on the departure deal.

Ministers have agreed to publish only a summary at 2pm, despite losing a vote last month over publishing the full deal. The prime minister’s official spokesman said this would be the “full reasoned positioned statement” in line with the commitments given by cabinet office minister David Lidington to the Commons last month.

Downing Street argues strongly that the summary will be sufficient information for any MP to make up their mind on the legal aspects of the deal before the upcoming five-day debate, and that it keeps to the protocol that full advice is seen as confidential between lawyer and client.

But Labour, which last month won a vote on a Commons motion obliging the release of the full advice, is to join forces with other parties, including the Democratic Unionist party (DUP), to try to pressure ministers to accede to their publication demand, using the ominous, if vague, threat of a contempt of parliament motion.

The shadow Brexit secretary, Keir Starmer, said he believed ministers would be in “really deep water” if they sought to thwart the Commons. Despite Lidington’s assurance to the Commons, MPs made clear this wouldn’t be sufficient, and Labour won on an opposition day motion to have all the legal documents published.

“If they don’t produce it tomorrow, then we will start contempt proceedings, and this will be a collision course between the government and parliament,” he told Sky’s Sophy Ridge.

“I accept that it’s exceptional to have that disclosed. It has happened in the past, but it is exceptional. That’s why we had a debate in parliament – to say: is this the sort of case where it’s so exceptional that it should be disclosed?”

Facebook Twitter Pinterest Geoffrey Cox, the attorney general, will answer MP’s questions on his legal advice. Photograph: Andy Rain/EPA

It is expected Labour will see how much detail is contained in the “legal position paper” – a precis of the advice given by Cox to cabinet – published on Monday, and in the attorney general’s answers to MPs, before deciding on a contempt motion.

In theory, a minister found to be in contempt of parliament could be suspended or even expelled from the Commons, though such sanctions are seen as extremely unlikely.

Any motion would be cross-party, with the DUP, May’s unofficial coalition partners, expected to join Labour’s efforts, along with the Liberal Democrats.

A few Conservative MPs have called for the full advice to be published, amid reports at the weekend that Cox had told the cabinet there was a risk the backstop arrangement could stay in place “indefinitely”.

Two strongly Leave-supporting Tories announced they wanted to see the the full advice. David Jones and Simon Clarke, who were both lawyers before becoming MPs, said the importance of next week’s vote made this vital.

Clarke said: “We are about to embark on the most significant debate in parliament for many decades. The functioning of the backstop and our ability to ever leave it will lie at the heart of it, and the advice the attorney general has laid before the cabinet is crucial.”

Boris Johnson used his latest Daily Telegraph column to add to the calls to publish the advice in full. The former foreign secretary said it was “outrageous that the public should be prevented from knowing the full legal implications of this appalling deal”.

A key issue for May is whether dissent spreads to more moderate MPs. One centrist Tory said: “There is good reason for advice to stay confidential. The issue here is trust. Given Brexit divisions, can this hold? Possibly not.”

Downing Street is publicly confident that the arrangement for Cox to answer questions should be enough to reassure even the most suspicious or curious MPs. “He will be there to answer any question any MP wants to put to him, so there is going to be full scrutiny. It’s important to note that we are making him available,” a No 10 source said.

May will also simultaneously begin a charm offensive to win over Conservative MPs in dozens of face-to-face meetings before the crucial Commons votes on the deal on 11 December.

In another Brexit wrangle, May and Jeremy Corbyn are still yet to agree the format for a mooted TV debate between the pair next Sunday. The Labour leader said he was happy to hold a head-to-head encounter on the BBC, while a No 10 spokesman said Corbyn’s “confected demands” meant he was trying to obstruct the process.