David Cameron's recent speech on immigration would appear to be aimed at frightening off Bulgarian and Rumanian immigrants who would have new rights to work in the UK from January 14.

But its main purpose must have been to ingratiate him with potential Ukip voters, because as a frightener it was weak and completely unnecessary. If Bulgarians or Romanians wanted to be here, they would have come. There were no visa requirements and they could work by declaring themselves self-employed.

Yet rather than frighten off EU immigrants, the recent speech from the Prime Minister is much more frightening to universities, and in particular new universities.

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He started off by stating that "net migration needs to come down radically from hundreds of thousands a year to just tens of thousands".

Students contribute the largest figure to these statistics – even though several select committees have proposed that they are counted separately. The problem is that, overseas students leaving the country are counted out, but as the average undergraduate degree is three years long (four in Scotland), there will always be more in the country than leaving. Thus, even though evidence suggests that by far the majority will leave, overseas students are still the largest contributor to the net migration statistics. And so that is the place where cuts have to be made to make the unrealistic net migration targets the Tories are craving.

Exactly where in the higher education system these cuts are going to hit was signalled loud and clear, if you know what to listen for. Cameron gives the game away by constantly describing the students he wants to see in the country as "the brightest and best".

As one of the 17 out of 22 Cabinet ministers who studied at Oxford or Cambridge, Cameron's view of what constitutes "brightest and best" is defined by his university experience, where the "brightest and best" from around the world are deliberately courted through schemes such as the Rhodes scholarship for future world leaders.

It works well, too. Get the "brightest and best" to Oxford or Cambridge (about the only places left where Britain is still a world leader), then steep them in ancient history and modern academic excellence – how could they fail to be impressed?

They return home with happy memories of a Britain still at the top of its game, where the plebs know their place, punters are people with punts and all is right in the world. So when they become leaders in their countries, Britain is their first-choice partner to split the proceeds of the invasion of some oil-rich trouble-maker. Or the supplier of choice of those wonderfully clever anti-personnel mines we make so well.

But times have changed. We have one of the most internationalised education systems in the world and new universities are some of the most active internationally. They bring a fresh, new-look British education system to the international stage – one that creates employable graduates; that uses its international cohort and extensive overseas partnerships to internationalise UK students as well as teaching international ones. It is a British education system that is seen as dynamic, lively, flexible and top quality, rather than an elitist ivory tower created from the dead tusks of colonialism. But these are not the type of international students Cameron wants.

Yes, statistics have shown that there was a 3% increase in visa applications to universities. But this hides the fact that 46% of international students in UK higher education have come through colleges in the UK, which have seen a 60% drop in visa applications. And, of course, newer universities with a widening access agenda are more likely to take students from college than more traditional ones. Each change the UK Border Agency brings in to the visa regulations has a disproportionate effect on newer universities.

But this will just be the beginning. If the Home Office is to reduce the numbers as it wishes, then it will have to be more deliberate and obvious in what it does. And without doubt that will mean some way of ensuring that only those who in Cameron's opinion are the "brightest and best" get in the country and keep out the rest! Yet international students are not just bright – they are one of the best things that has happened to our universities in many years.