The compromise Brexit deal being discussed by Theresa May and Jeremy Corbyn – with the UK staying in a customs union – would deliver an £80bn hit to the economy after 10 years, economists have said.

People would be an average of £800 worse off, GDP would shrink by 3 per cent and there would be £13bn less a year to spend on public services, compared with EU membership, the analysis found.

“It would involve significant non-tariff barriers that would hinder trade, particularly in services. That would be a material economic burden,” the National Institute of Economic and Social Research (NIESR) said.

The study – the first into the impact of the mooted cross-party deal – was seized on by supporters of a fresh Brexit referendum as proof that a customs union must not be seen as a “soft option”.

They pointed out the £13bn annual loss in Treasury spending power was greater than the cost of Labour’s flagship pledge to axe student tuition fees, which has been put at £11.2bn.

“A customs union deal is not as damaging for our economy as a no-deal Brexit,” said Rachel Reeves, a Labour supporter of the People’s Vote campaign.

“But it is a mistake to regard it as a soft option – let alone a fix-all for a political crisis that has its roots in promises that can’t be met, real costs that have been ignored.”

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The report, for People’s Vote, comes as talks continue between Labour and the Conservatives, although the two sides remain far from agreement on a deal that could be put to the House of Commons.

Labour is demanding a permanent customs union, as well as single market alignment, while the Tories have conceded only a temporary arrangement – possibly covering only goods and not services.

But the NIESR predicted the cost of such a deal, after a decade, would be greater than the entire annual budget of the Department for Business, Energy and Industrial Strategy.

Investment and productivity would be hit by “higher barriers to trade in services” and Britain would pay the price for lower immigration outside the single market.

“We estimate that GDP per head would be around 2 per cent lower than it would have been had the UK stayed in the EU, equivalent to around £800 per person per annum in today’s prices,” its report said.

Garry Young, the think tank’s director of macromodelling, added: “Leaving the EU for a customs union will make it more costly for the UK to trade with a large market on our doorstep, particularly in services, which make up 80 per cent of our economy.

“We estimate that all regions will be adversely affected and that there will be fewer resources available to pay for public services.”

The government has not modelled the impact of a customs union Brexit, but it did conclude Ms May’s Brexit proposals – now apparently dead – would cost 3.9 per cent of GDP after 15 years.