The government’s long-expected post-Brexit immigration plan will have no reference to the Conservative manifesto pledge to reduce net migration down to the “tens of thousands”.

Whitehall sources confirmed to The Independent that the target long-championed by Theresa May as home secretary and prime minister does not appear anywhere in the document.

The target will still exist as a manifesto pledge until the next election at least, but its absence is a clear sign policy has now moved away from the numbers-based approach backed by Ms May.

Publication of the white paper was pencilled in for Wednesday but is yet to be confirmed, amid reports that Ms May is at odds with ministers over her desire to frame the new system as an immigration crackdown.

Instead there is a push for the government’s new approach to be positively framed as a system serving the skills needs of the UK economy as it leaves the EU.

The news is a victory for The Independent’s Drop the Target campaign, launched back in April 2017 with Open Britain, to see the blunt policy ditched.

The writing has been on the wall for the target – set out in Tory manifestos from 2010, 2015 and last year – since Ms May’s authority was critically weakened after losing her party’s majority at the 2017 election.

Several ministers have indicated they do not fully support it, including home secretary Sajid Javid, his predecessor Amber Rudd, now pensions secretary, and international trade secretary Liam Fox.

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Discussing the white paper, a Whitehall source said of the target: “It’s not in there, and it won’t be unless someone slips it in at the last minute.”

Instead the paper will talk about reducing migration to “sustainable levels”, a phrase used recently in an interview by Mr Javid, who has also distanced himself from the “hostile environment” policies once backed by Ms May.

People want to end free movement, and the document does talk about reducing net migration to sustainable levels, but it’s more about what that will actually look like Whitehall source

A leak to The Sunday Times at the weekend focussed on potential reductions of numbers in EU migrants that the plan would bring.

But The Independent’s source explained that the new system was a “clear step towards changing the shape of the immigration debate away from numbers and towards an approach that ensures the UK has the skills it needs”.

“People want to end free movement, and the document does talk about reducing net migration to sustainable levels, but it’s more about what that will actually look like,” the source added.

The process of pushing the immigration white paper through has been arduous, requiring approval from a number of departments including the Treasury and the Department for Business, run by Philip Hammond and Greg Clark respectively – both who have prioritised reducing the impact of Brexit on the economy.

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Elements of the plan to have already appeared in the press indicate there will be no cap on highly skilled migrants from anywhere in the world.

Medium-skilled migrants will be allowed in if they have a job paying at least £30,000 a year, but migrants with skills Britain needs will be granted visas on a lower salary.

Low-skilled workers will get short-term visas of up to a year if they are from a country that is a “low risk of immigration abuse”, while students will be granted six months of study leave and can switch to a skilled worker’s visa three months before the end of their course.

Ms May championed the target when she was running the Home Office and fought battles with then-chancellor George Osborne, who was pushing for it to be lifted.

At the time The Independent launched its campaign to ditch the target, Ms May’s allies were certain it would be retained in a post-Brexit plan, saying it was “unfinished business” from her six years at the Home Office.

But the departure from the target now marks the decline in Ms May’s authority, with her pledging only last week that she would not lead the Conservatives into the 2022 election, as she fought to save her job in the face of a backbench coup.