A trade deal with the United States will not make up for the hit to Britain's economy from curbing migration from the European Union, according to leaked government documents obtained by BuzzFeed.

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

Several immigration policies were analysed in the papers to assess what impact they would have on UK finances. The research revealed 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 likely from a US trade deal.

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

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 BuzzFeed.

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.

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

"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."

A government spokesperson 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."