A leaked document has exposed how Theresa May “sabotaged” a Government-wide plan to explain the benefits of immigration to the British public.

The Cabinet Office paper seen by The Independent suggests Ms May used her political clout to prevent the bid to explain the “positive impacts” immigrants bring the economy and NHS.

Critics now claim the incident reveals how the Prime Minister will be prepared to put political considerations on immigration ahead of the national interest going into Brexit talks.

Ms May has taken a hawkish approach to immigration since making ending free movement the cornerstone of her Brexit plan, to the extent that she has even clashed with pro-Brexit ministers over her hardline stance.

But despite having to admit this week that free movement may continue well past 2020, she still refuses to ditch a promise to lower immigration to the "tens of thousands".

The Cabinet Office document leaked to The Independent reveals that the Home Office, then run by Ms May, refused to back a cross-departmental drive during the EU referendum about “the positive impacts that migration can have on the economy as a whole and on individual public services.”

The aim was to “more effectively counteract the arguments of those advocating Leave.”

In the report to Sir Jeremy Heywood, the Cabinet Secretary, one of his officials wrote: “Despite attending the initial cross-Whitehall meeting, the Home Office haven’t really engaged with this work at all - I assume because they do not think the Home Secretary [Ms May] will agree to it.”

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The document concluded that without “a political decision by the Home Secretary,” the Government could not go further than its previous statements on the number of skilled EU workers in public services; the fiscal contribution of EU migrants and their “broadly neutral impact” on public finances and public services.

It was written on 5 May last year, as the Leave camp put immigration at the heart of its referendum campaign and eclipsed Remain’s warnings about the economic risk of Brexit, dubbed “Project Fear.” Immigration was widely seen as tipping the balance in favour of Leave.

The leaked report was seized on by MPs involved in Open Britain, the successor to Remain, which is running a Drop the Target campaign with The Independent urging the Government to abandon its goal of reducing net migration to under 100,000 a year.

Chuka Umunna, the Labour MP and former shadow Business Secretary, said: “An ideological Prime Minister undermined the referendum campaign by failing to make the case for the value of migration. She helped sabotage Remain by refusing to properly engage with the migration debate.”

He added: “She is now compounding the cost by putting extreme migration cuts ahead of economic growth and jobs, leaving the single market based on the fantasy that the same benefits can be secured outside of it. It’s time to drop the tens of thousands migration target.”

Pat McFadden, Labour’s former shadow Europe Minister, said: “This document reveals that even though Number 10 wanted to make a more positive case about the effects of migration, their view was the Home Secretary was so hostile she wouldn’t take part. Immigration was a huge issue in the campaign. This could have made a difference.”

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Norman Lamb, the former Liberal Democrat minister, said: “Throughout the referendum, the Remain campaign was fighting with one hand behind its back thanks to the appalling cynicism of Theresa May. By pretending to be in favour of EU membership while refusing even to engage with the debate about migration, she could not have done a better job for Leave if she had been working for them secretly.”

But May allies dismissed the claim that she sabotaged the Remain campaign, pointing out that she endorsed it. One said: “People who lost the referendum are trying to pin the blame on someone else. They should stop re-fighting the campaign, move on and support the Prime Minister’s efforts to regain control of migration, which is what the public voted for.”

Her allies insisted that David Cameron and George Osborne, not Ms May, decided not to return the Leave camp’s fire on immigration. They believed it would dilute their message on the economy and merely draw more attention to immigration.

Mr Cameron rejected pressure from Labour and Liberal Democrat figures in the Remain campaign to make a speech about immigration. Some former Cameron aides now believe it was a mistake not to tackle the issue head-on.

The leaked report will fuel the debate about Ms May’s actions during the referendum. Sir Craig Oliver, who was Mr Cameron’s director of communications, claimed in a book that the then Home Secretary failed to back Remain on 13 occasions and was described by some in the campaign as “an enemy agent” and “submarine May”.

Critics claim Ms May’s position as a reluctant Remainer was designed not to alienate either Remainers or Leavers in order boost her prospects in a future Tory leadership election. She delighted Leavers by saying EU membership made it harder to control “the volume of immigration” and that she did not believe “the sky will fall in” after a vote for Brexit.

In 2015, Ms May said the evidence showed that while selective and controlled immigration had benefits, “at best the net economic and fiscal effect of high immigration is close to zero.” She argued that there was “no case, in the national interest, for immigration of the scale we have experienced over the last decade.” She added: “When immigration is too high, when the pace of change is too fast, it's impossible to build a cohesive society.”

Ms May has refused to remove international students from the net migration totals, even though that would give the Government a quick win in cutting the numbers. This has put her at odds with Cabinet colleagues, including Boris Johnson and Liam Fox, who have suggested that students should not be included in the cap.