The post-Brexit customs arrangement favoured by leading Brexiteers could cost businesses up to £20bn a year, HMRC has said.

The organisation’s chief executive, Jon Thompson, told MPs the option of a “highly streamlined customs arrangement” would be significantly more costly than a more comprehensive customs partnership – the other option ministers are considering.

He said HMRC had estimated the cost to businesses of having to complete customs declaration forms after Brexit as £32.50 per shipment. There are around 200 million exports from Britain to the EU each year, meaning the total cost of customs declarations for UK firms would be £6.5bn each year. EU companies would have to pay a similar amount, taking the overall cost to £13bn.

Taking steps to meet EU regulations would cost businesses “several billion pounds more”, Mr Thompson said, raising the total cost of the customs arrangement to between £17bn and £20bn.

He told the Commons’ Treasury Committee: “I think you need to think about the highly streamlined customs arrangement costing businesses somewhere in the late teens of billions of pounds to operate – somewhere between £17bn and £20bn. It’s that sort of order and the primary driver is the fact there are customs declarations.”

Ministers are currently considering two options for managing imports and exports after Brexit. The first option, the “highly streamlined customs partnership”, would seek to allow the frictionless transfer of goods across the border by using technology to reduce the need for checks. This has been described as maximum facilitation, leading the arrangement to be dubbed “max fac”.

The other option, a more substantive customs partnership, would see the UK and EU collect tariff duties on each other’s behalf. This would, in theory, allow goods to cross the border without the need for comprehensive checks.

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Mr Thompson said the customs partnership option would be significantly less costly for businesses, with a maximum cost of £3.4bn. In reality, he said, the model could be cost neutral, because businesses would be able to claim back any tariffs they incur.

The HMRC boss had earlier told another committee of MPs that the max-fac model would take at least three years to implement – meaning it would not be in place by the end of the Brexit transition period. The customs partnership could take up to five years to introduce, he said.

The max-fac option is favoured by leading Brexiteers such as Boris Johnson and Michael Gove, who believe it would result in a cleaner break from the EU. Remain-supporting ministers, including Ms May, prefer a customs partnership.

The prime minister has split her cabinet’s Brexit subcommittee into two groups to investigate the respective customs options. David Davis, the Brexit secretary, Greg Clark, the business secretary, and Karen Bradley, the Northern Ireland secretary, are investigating the max-fac option.

Mr Gove, the environment secretary, Liam Fox, the international trade secretary, and David Lidington, the Cabinet Office minister, are looking into the customs partnership.

Downing Street dismissed the HMRC figures as “speculation”.

Ms May’s spokesman said: “The prime minister has asked for work to be done on both customs models. That work is ongoing, and therefore any speculation about work ongoing, is just that.”

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But anti-Brexit campaigners leapt on the HMRC revelation as evidence of the risks of abandoning plans for a comprehensive customs partnership.

Labour MP Jo Stevens, a supporter of the Best for Britain campaign, said: “This is Boris’s 20 billion Brexit bombshell and it threatens to blow up our economy.

“This shocking evidence from the chief taxman today shows that Brexiteers don’t care about the carnage it will cause to the economy.