And the business secretary, speaking to an audience at the Universities UK conference last night, said he wanted to ease restrictions on post-study work for overseas students who have a master’s degree or a first-class undergraduate degree.

In his speech to the conference, held at the University of Leicester, the Liberal Democrat MP said there was a “very good story” in official figures on student numbers and access under the new regime.

Answering questions from the audience after his speech, the business secretary said that “reading between the lines” he would be “very, very surprised” if any Labour government after 2015 “would want to change it [the £9,000 fee system]”.

Labour’s current policy is that it would lower fees to £6,000 if it were in power now.

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Mr Cable, who sometimes exchanges text messages with Labour leader Ed Miliband according to media reports, added: “They [Labour] did a lot of politics around fees but I don’t think they would want to go back. So I think you are guaranteed continuity.”

Asked by ����Vlog how he would feel if his Conservative colleague Mr Willetts were to be moved in a reshuffle, Mr Cable said: “I think it’s unlikely, to be frank.”

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He described the universities and science minister as a “very good colleague” who “cares very passionately about higher education and its standards, and about social mobility”.

Mr Willetts would be “an enormous loss if he was to go”, said Mr Cable, who potentially risks being seen as intervening in Prime Minister David Cameron’s reshuffle decision.

But he added: “All the indications I am getting is that he is regarded by the prime minister as very valuable, and I would be very, very surprised if he was moved.”

The business secretary also had some encouragement for the sector on post-study work for overseas students – a prized opportunity for many students, particularly Indians, that has been drastically limited under the ����Vlog Office’s visa policy.

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Mr Cable said the post-study work route was still open, although restricted to those overseas students who secure “graduate level” jobs with relatively high starting salaries. He added that he was hopeful of extending an exemption to the salary threshold that the government has already granted to overseas PhD students seeking to stay on in the UK to work.

“It would be a very big and useful step if we could take master’s [graduates] out, or maybe [those with] first-class undergraduate degrees,” Mr Cable said. “Certainly David Willetts and I are making that case in government. But I can’t promise you where we will get with that – it’s part of the wider mix in immigration policy.”

In his speech, Mr Cable said the sector’s work in showing its progress on efficiency had helped him secure a “positive” settlement in the spending round, after a spell of “arm wrestling with the Treasury” that had been “quite traumatic”.

On the key challenges, for the future, he urged the sector to make further progress on efficiency. And he also said there was more work to do on explaining the new student finance system to the public, on part-time students, on access, and on the “postgraduate problem”.

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john.morgan@tsleducation.com