Concern over immigration was one of the most important factors for those who voted for Brexit, yet we already have the power to take back control of the free movement of EU citizens to the UK – we just aren’t using it. Both major political parties’ front benches, and even cabinet members, are divided when it comes to whether Britain should remain in the single market, which entails allowing free movement of people within the EU. But the reality of immigration in Britain today is a far cry from the public’s perception.

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We lost control over our borders almost two decades ago. In 1998, Tony Blair removed exit checks. Nobody checks your passport once you have gone through security at an airport, as they do in virtually every other country in the world. As a result, we have no robust way of knowing exactly who has left this country. The government cannot even provide figures for illegal immigrants in the UK who are not detained to the nearest quarter of a million.

Why doesn’t the government implement these exit checks? Every person entering and leaving the country needs to have their passport scanned, EU and non-EU alike; only then we will have true control of our borders. Exit checks would not only act as a deterrent but would give us accurate migration data, identify overstaying individuals and give us correct figures when it comes to international students.

The government reintroduced exit checks in 2015 – but these fall well short of the physical, visible checks after security, which are airport-enforced. And the government refuses to release any statistics from these checks for one reason: they would demolish the anti-immigration stance taken by this government, the prime minister and the home secretary.

It would dispel the myth that up to 100,000 international students overstay their visas every year. Just this week – after parliament went into recess – the Office for Statistics Regulation sneaked out a report saying that we cannot rely on the immigration statistics for international students, as they are based on completely inaccurate international passenger survey (IPS) figures. Surveys are not even carried out after 10pm, when many international flights leave. The government itself has now said they are to be treated as “experimental”.

I challenged the government on why we were not availing ourselves of this directive – and I got no response

But the IPS has been used to justify treating international students as immigrants and as part of the target to reduce net migration to the tens of thousands. There is no logic to this. Our competitor countries – the US, Canada and Australia – classify international students as temporary residents when calculating their figures. Instead, we give the perception that we want to cut down the number of international students when that should not be the case – we should be welcoming the money and expertise they bring.

The “tens of thousands” figure itself was plucked out of thin air with no regard for what the country actually requires. We have virtually the lowest level of unemployment – 4.5% – and the highest level of employment on record. Without the immigration that we have, we would have a labour shortage, both skilled and unskilled.

There is a perception that immigrants are mostly taking unskilled jobs and lowering wages for the domestic population, but the evidence points firmly in the other direction. At Russell Group universities, up to 39% of academic staff are foreign; over 26% of our NHS doctors are non-British; and the heads of many of our leading companies are immigrants, including the chief executives of Jaguar Land Rover (Ralf Speth) and Reckitt Benckiser (Rakesh Kapoor).

But the biggest deception is this: we could easily have taken back control of our borders already under European Parliament and Council Directive 2004/38/EC, which allows EU member states to repatriate EU nationals after three months if they have not found a job or do not have the means to support themselves. In this month’s debate on the House of Lords EU subcommittee report on EU migration, I challenged the government on why we were not availing ourselves of this directive – and I got no response.

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Other countries, such as Belgium, regularly repatriate thousands of individuals based on this directive. If the public knew we had this ability, perhaps the fear that exists would dissipate. Why is the government not using it, and why is the British public not aware of it?

Anti-immigration messages and perceptions have been driven by the prime minister and former home secretary Theresa May, as well as the present home secretary, Amber Rudd, who are both economically illiterate when it comes to the necessities of the movement of people, quite apart from being negligent over the security of our country. We could take back control of our borders and re-implement exit checks within months, if the government was determined to do it.

If the British public were aware of the reality of immigration – be it control of our borders, be it potential labour shortages, or be it the ability to repatriate EU citizens – then they would soon realise that the Brexit emperor has no clothes.