The British economy will be hit by a “permanent cost” of more than £25bn a year if it decides to withdraw from the EU customs union, a new government adviser on Brexit has said.

Raoul Ruparel, who has been hired by David Davis to provide expertise on the process of leaving the EU, said he believed there was no question of the UK staying in Europe’s free-trade bloc.

But he admitted that leaving the customs union, inside which EU countries negotiate trade deals collectively and set common external tariffs, would reduce GDP by between 1 and 1.2% in the long term.

Ruparel’s comments, made before he was appointed to the senior government position, could provide ammunition for Labour MPs who have challenged the government’s trade secretary, Liam Fox, to prove the benefits of such a move.

A group of 53 Labour MPs, led by shadow Brexit secretary Keir Starmer, have sent a letter organised by the campaign group Open Britain demanding a “rigorous and publicly available cost-benefit analysis” to demonstrate why it would be the best option.

So far Davis and Theresa May have not said whether they believe Britain ought to withdraw from the union, with some ministers in government warning that the move would cause a huge extra burden on exporters.

But Fox has signalled that he supports withdrawal to allow the government to negotiate its own free trade deals.

Ruparel, who will be heavily involved in the process, made clear that he believed Britain would have to leave the bloc, arguing “this ship sailed some time ago”.

“The only real question then is why this is even a ‘live debate’ in Whitehall?” he wrote. “It is concerning that, at this stage, the UK government seems to still be debating the most basic tenets of Brexit when the time is upon us to be drafting a detailed approach.”

In the revealing analysis during the summer, he pointed to in-depth research by his thinktank, Open Europe, about the issue.

“What we found is that, in the long run (up to 2030), there will be a permanent cost to leaving the customs union,” the analysis said. “This cost is around 1% to 1.2% GDP.”

The additional costs were linked to the administrative burdens that would result from something known as “rules of origin”, under which the UK would have to prove that goods being exported into Europe were produced locally.

“But this cost is clearly not prohibitively high,” he said, adding that Norway and Switzerland were outside the bloc but had significant levels of trade with the EU. Ruparel said the alternatives were “less palatable”.

The Turkish model of being inside the customs union but outside the single market would allow immigration restrictions but “would mean the UK could not negotiate its own free trade deals and would have to accept whatever the EU agrees to with other parties,” he said.

Adopting a different Norway-like model in which Britain was in the customs union but also had a free trade deal would be hardly different to remaining in the EU. “The former would be economically disruptive and the latter would be politically explosive,” he wrote.

The intervention could alarm senior figures inside the Treasury, with ministers telling the Guardian that the reality of leaving the bloc will be significant costs for business that had to be addressed.

A spokesperson for the Department for Exiting the EU said the comments were not made on behalf of the government, saying: “This article was written before Mr Ruparel joined the department and reflects his work at Open Europe.”

A Labour MP, Emma Reynolds, said Ruparel’s comments made it more urgent for the prime minister to outline the direction that Britain would take. “The government needs to level with the British people that there are big trade-offs in this process and it is not going to be an easy thing to achieve,” she said.

Prof Jim Rollo, deputy director of the UK Trade Policy Observatory, added: “£25bn is not a small amount. The main advantage of leaving the customs union is that we can make our own trade deals around the world but there is no guarantee that these will be any better than those negotiated by the EU.

“The other 27 countries have a combined GDP that is almost six times that of the UK’s so they are offering other countries access to a much larger market and have more negotiating clout.”

The letter from Labour MPs, including the former home secretary Alan Johnson and former leadership candidate Liz Kendall, said they would have to conclude Fox was being “disingenuous about hypothetical future trade benefits and in denial about the real cost” unless he could produce evidence of the benefits of such an exit.

Meanwhile Starmer and the shadow foreign secretary, Emily Thornberry, will write to Davis on Wednesday with a list of 170 questions that they say remain unanswered by the government on Brexit – one for each day until article 50 is triggered in late March.

There are tensions within government departments about whether May will push for a hard Brexit in which immigration controls will be heavily prioritised over economic links.

Reports suggested that government was still using a warning of a £66bn a year cost in tax revenues if Britain leaves the single market, despite the figure being based on a Treasury forecast from April. A Downing Street spokesman warned against attempts to “reheat the arguments” of the EU referendum and distanced May from the suggestion.

Meanwhile the government has been accused of trying to avoid scrutiny of its Brexit strategy by creating a parliamentary committee that is too big to do its job properly.

The Guardian can reveal that Davis has produced a report for Cabinet colleagues that hits back at civil servants who are making the claims.

In a paper that will be seen by Cabinet ministers on Wednesday, the Brexit secretary says it is extremely unlikely that the UK would end up with the worst case scenario of having to trade with the EU under WTO rules. He also promises that ministers would act to mitigate the impact if that did happen.

May has tabled a last-minute amendment to Labour’s opposition day debate in parliament. Jeremy Corbyn’s party has laid down a motion calling for MPs to be able to scrutinise Brexit plans before article 50 is triggered in March.

The prime minister has joined Davis, the chancellor Philip Hammond and the home secretary, Amber Rudd, to add a sentence calling for parliament to respect the decision of the 23 June vote in favour of Brexit. It also says that politicians must not “undermine the negotiating position of the government”.

A Downing Street aide said: “The government is focused on delivering on Brexit. We have always been clear that while we should do nothing to undermine our negotiating position, parliament has an important role to playand this motion reflects that.”

In a plan to be officially announced on Wednesday, 21 MPs will sit on the new cross-party Brexit select committee. The committee will be almost double the size of almost every other Commons select committee following a deal struck between Conservative and Labour whips.

Some senior MPs have claimed that the committee has been made deliberately large so that it is less effective at scrutinising the government’s strategy and less able to reach a consensus.