The revelation provoked fury last night from Brexit campaigners. It comes after another internal leak from Whitehall to a pro-EU website claimed cutting immigration would harm the economy.
This has led to claims that Remainers within the Government are trying to water down the benefits of Brexit so that voters may be persuaded to reverse the referendum result.
The latest leaked impact assessment document suggests EU workers will be given “preferential” treatment if Britain wins a free-trade deal.
According to reports, the economic analysis has been drawn up with the support of Home Secretary Amber Rudd, who was a leading figure in the Remain campaign and has been accused of trying to frustrate Brexit within the Government.
A “flexible migration” scenario, branded as being a “midway point between strict policy and continued labour mobility”, would see EU workers having to earn £20,500 to come to the UK, according to the report.
It noted: “The Treasury believes a relevant factor to be considered when appraising the economic impact of various end states is the integration with migratory flows.
“There are a number of possible policy scenarios on which the Home Secretary has been consulted.”
The analysis also revealed the benefits of a “no-deal” scenario, which would mean migration controls will be tougher if the UK exits the EU without a trade deal, leading to 90,000 fewer EU migrants a year.
In a no-deal scenario, migrants would need to have degrees, a job offer and earn at least £30,000, which would bring them into line with visa requirements for non-EU workers, the report said.
Leave Means Leave chairman Richard Tice reacted angrily to the leak.
“Every soft announcement and revelation from Remainer civil servants and politicians in the Government is contrary to the democratic vote which was to take back control of trade and borders,” he said.
“It is increasingly clear that the Prime Minister must move towards the Leave Means Leave position of a Canada-plus style deal and World Trade Organisation rules so that we can properly take advantage of Brexit and not be handcuffed to the EU forever.”
Former Labour MP and Brexit campaigner Tom Harris said: “Britons will not accept a Brexit that does not cut immigration.”
He went on: “We can see where the Remain camp hope the negotiations will take us: To a position where any increase in national sovereignty – payments to the EU, migration, the ability to develop our own regulations – are so modest that it will dawn on the populace that it hardly seems worth the effort of leaving the EU at all.”
Former Tory cabinet minister Priti Patel said: “The most important thing about any modelling is that we want to ensure we do what we promised the British public – take back control of our immigration policy.”