Securing a trade deal with the United States will fail to make up for the hit the economy will take from curbing migration from the European Union, according to leaked government documents.

New customs arrangements, border checks and the loss of market access in certain sectors on top of the impact of immigration reforms will cause the main damage to the economy, the Brexit analysis prepared for the Department for Exiting the EU (DexEU) found.

Several immigration policies were analysed in the papers to assess what impact they are likely to have on UK finances, according to BuzzFeed News.

Passengers going through the UK Border at Terminal 2 of Heathrow AirportPassengers going through the UK Border at Terminal 2 of Heathrow Airport (Steve Parsons/PA)

The research found replacing free movement with a system similar to that in place for non-EU citizens would have a bigger effect than the 0.2% boost that a US trade deal could counteract.

Looser restrictions would still cancel out the benefits of increased trading across the pond.

The study, EU Exit Analysis – Cross Whitehall Briefing, found the combined effect of trade barriers and lower immigration could mean UK borrowing is tens of billions of pounds higher in 2033-34 than under the status quo even when a US trade deal and savings from quitting the EU are taken into account, according to the website.

It comes after Prime Minister Theresa May dismissed the significance of separate findings in the study leaked earlier in the week.

The documents indicated that any outcome from Brexit would leave Britain worse off.

Liberal Democrat leader Sir Vince Cable said: “The view that restricting immigration is a positive thing, something this Conservative government have only encouraged, has been starkly contradicted by their own analysis.

“This analysis shows a fall in EU migration is far from cost free. The resulting loss of skills and government revenue means any trade deal with the US won’t even begin to bring in the cash lost by a clamp down on migration post-Brexit.

“As the government’s own evidence against their blinkered hard Brexit agenda begins to mount, the British people must be given their say on the final deal with the option to exit from Brexit.”

Liberal Democrats leader Sir Vince Cable said British people must be given their say on the final deal with the option to exit from Brexit (Andrew Matthews/PA)Liberal Democrats leader Sir Vince Cable said British people must be given their say on the final deal with the option to exit from Brexit (Andrew Matthews/PA)

The Scottish National Party’s Europe spokesman Stephen Gethins MP said immigration was “vital” to the Scottish and UK economy, adding: “It is clearer than ever that a hard Brexit driven by ideological Tory obsession with immigration would be catastrophic for jobs, the economy and frontline services.

“In the face of such overwhelming and increasing evidence, Theresa May must put the interests of the country before the interests of her party’s Brexiteers.

“The Leave campaign promised that Scotland would receive powers over immigration after Brexit – with Cabinet Minister Michael Gove saying that levels of immigration would be ‘for Scotland to decide’. As the UK heads towards the self-imposed exile from Europe, it’s time the UK government made good on that pledge, so that Scotland is no longer a passenger in this slow motion Brexit car crash.”

A government spokesman said: “The UK will remain an open and tolerant country; one that recognises the valuable contribution those with skills and expertise make to society while also ensuring there is control of the overall numbers of migrants that come to the UK.

“As we leave the EU, we will forge new and ambitious trade deals around the world, with trading partners old and new.”