Scottish Conservative MPs are lobbying Theresa May to drop students from immigration figures and develop a generous post-Brexit visa scheme for universities as they begin to wield their power in Westminster.

Sky News has learnt that the recently-elected group of Scottish MPs has held a private meeting with Amber Rudd, the home secretary, to impress on her the importance of dropping students from the immigration target.

They have also been meeting immigration minister Brandon Lewis - most recently on Wednesday - to discuss what they want from a post-Brexit immigration system to accommodate the needs of universities and research facilities in Scotland.

Universities are worried that Brexit will deter EU students from coming to study in the UK and have argued that removing students from immigration numbers will send a powerful signal that talent is welcome in the UK.

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The issue is a source of tension within the party and could blow up in the New Year when MPs consider a bill to set up a post-Brexit immigration regime.

Mrs May is resisting stripping out students for fear of being accused of fiddling the figures to hit her target of reducing immigration to the tens of thousands. It stood at 230,000 in the year to June.

Image: Ruth Davidson with the party's then newly-elected MPs in June

But many MPs, including the 12-strong Scottish group of Tories, are pressing her to back down.

The Scottish MPs, elected in the snap election, are a formidable bloc who could overturn her working majority.

One source familiar with the talks between the MPs and Ms Rudd told Sky News: "They weren't threatening but made very clear their views."

The Scots have already claimed credit for a series of major "wins" in the Budget after "bending" the ear of the Chancellor in the run up to the speech.

Philip Hammond said he had bowed to demands that Scotland's national police and fire services have their annual £40m VAT bill refunded in the future.

They also secured help for the North Sea oil industry, City Deal funding for the Borders, Stirling and Tayside and a freeze on duty in Scotch whisky.

John Lamont, MP for Berwickshire, Roxburgh and Selkirk, told Sky News he and colleagues were working hard to get the best deal for Scotland's higher education sector.

Image: John Lamont says he wants the 'very best deal for Scotland'

He said: "Clearly there is a Scottish perspective on Brexit and our job as Scottish Conservative MPs here in Westminster is to work with our colleagues, work with colleagues within government to get the very best deal for Scotland as part of that. And we are very clear there is a deal to be done."

George Freeman, former science minister and head of Mrs May's policy board, has joined the Scots, telling Sky News in an exclusive interview that he too wants students taken out of immigration.

"I think it is very important that we signal we are open to Britain as an education beacon of the world. It is one of our great industries. I want to bring more students here," he said.

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"I think we are going to have to send a signal through this that we don't see Brexit as a moment to shut down our student borders and I'd like us to signal very loud that we want our students to go around the world and we want global students to come here and if that means taking student numbers out of the immigration cap, so be it."

He also said Mrs May must keep paying into the Erasmus exchange scheme beyond Brexit to prove to young people that "Brexit isn't a triumph of the Alf Garnet wing of politics where we turn our back on Europe".

The Prime Minister has said the UK will continue in Erasmus until at least the end of 2020, but hasn't committed to the scheme beyond the end of the decade.

Image: Theresa May has resisted removing students from immigration figures

But she has been immovable on the issue of removing students from immigration figures, despite pressure from a number of her cabinet ministers including Ms Rudd and education secretary Justine Greening.

One senior figure told Sky News that the cabinet expected some sort of discussion over the matter before the summer recess but said Mrs May has kept it off the agenda.

The tens of thousands target was included in the 2010, 2015 and 2017 manifestos, but successive governments have failed to meet it.

Net migration fell by over 100,000 in the year to June following the referendum but is still well off that Conservative target at 230,000. The number of students coming to the UK fell by 23,000 to 141,000 over the same period.

But many Brexiteers are backing Mrs May.

The campaign group Leave Means Leave published a paper last month saying students should continue to be counted in the net migration statistics as it outlined a plan to drastically reduce migration into the UK.

There would be a moratorium on EU migration for low-skilled work and a permit skill for graduate level or highly skilled migrants.

Sir Gerald Howarth, board member of Leave Means Leave, said: "The numbers are still far too high and this must be addressed as soon as Britain leaves the EU in March 2019.

"The Government should adopt a British work permit system to cut net migration to sustainable levels last seen in the mid 1990s."