Eric Thomas, president of UUK, told journalists on 17 May that his organisation would be writing to David Cameron before the next set of net migration figures were published on 24 May.

Those figures, from the Office for National Statistics, will be a test of government progress on implementing the Conservatives’ pre-election pledge to reduce net migration to the “tens of thousands”.

Any increase in net migration might prompt the government to further tighten the visa regime for non-EU students – and British universities believe that existing measures have already damaged their appeal to overseas students and hindered growth in what could be a strong market for the UK economy.

Alternatively, if the government was to remove university-sponsored non-EU students from the net migrant count, that might offer it a route to reach the “tens of thousands” target. The move would also ease the pressure on a valuable income stream for universities.

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Professor Thomas, vice-chancellor of the University of Bristol, warned that the UK was “in real danger of sending out the wrong message to the world about whether or not we welcome students and academics from outside the EU.

“We’ll be writing to the prime minister to make the request to remove students from the net migration figures and to outline to him our concerns.”

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Overseas students “contribute hugely to the UK academically, culturally and financially,” he added.

UUK issued a briefing document stating that competitor nations such as Australia, Canada and the US “take a different approach and categorise international students as temporary or ‘non-immigrant’ admissions”.

Professor Thomas highlighted the case of Aston University, where applications from Indian students for 2012-13 have fallen by 40 per cent.

He conceded that applications from non-EU students have increased overall across all institutions, but said it was too soon to say how this would translate into student numbers as “applications have got to cross the border yet”.

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john.morgan@tsleducation.com