The EU Referendum is finally here. By the end of the week we will know whether Britain will Remain or Leave. Any Remain supporter will be concerned about polls in recent days showing each side by side or with Brexit edging ahead – although we should recall our bitter memories last year of how polls did anything but predict the outcome.

A key issue in the debate remains immigration. While the economy is Remain’s greatest strength, there is little doubt that immigration has been its weakness. Brexiteers continue to make the case for Leave around the idea that Britain can better control its borders outside the EU than remaining within it.

This is a simple pitch for a complex area. The UK’s immigration rulebook is currently over 2,000 pages long. The rules cover everything from student visas and marriage to non-EU workers and British citizenship. And that’s before we have the extensive case law.

Migration does not have simple answers. If the aim is to deny entry to anyone born abroad, then leading Leave campaigners from South East MEP Dan Hannan (born in Peru) to dual US and UK citizen Boris Johnson (born in New York) become issues. Or if denying entry to non-British spouses were an aim, there’s then Nigel Farage’s German wife. My point is that keeping non-British or foreign-born citizens out to ‘take back control’ isn’t a simple matter – and leading Leave campaigners don’t support it anyway for reasons both political and perhaps personal.

Their case is that Brexit means taking back control of Britain’s borders. So is it true? We must counter this central argument better if we want to win the vote on Thursday.

But we can do this – and from our progressive Labour values. Let me explain.

Vote Leave claims that if Britain left the EU we could launch an Australian-styled points-based system of immigration control. Britain could keep its doors open to the most talented and highly skilled benefiting economically, but without exposing us to unlimited migration.

The problem is that this is not how the points-based system works in Australia. Their aim was to increase immigration – if any migrant met set criteria, the door was wide open to admit as many that wanted to come settle in Australia. Even MigrationWatch – yes, even them – are opposed to setting up Australia’s system in the UK because it would likely lead to even more migration than less.

A more sensible approach is to have controls on the skills and work that Britain wants to attract – like nurses, university lecturers and other highly skilled workers – but subject to a cap. The good news is Britain already has this, at least for non-EU citizens. And we’ve had it in place for over a decade thanks to a Labour government. I know – I had to satisfy it in order to settle in Britain before becoming a British citizen in 2011. Don’t believe me? See this guide to the UK’s point-based system.

Vote Leave also claims exiting the EU would mean the end of the free movement of EU citizens. The key point here is ‘free’ movement isn’t free – there are controls. The issue is enforcing existing rules better and not that no such rules exist.

For example, ‘free’ movement is for workers, not benefit claimants. No EU citizen arriving in Britain can claim benefits for the first three months – and if there is no job or realistic prospect of work, they can be deported within six months. Or in other words, they may be required to leave in six months just like any other tourist must. Simple as that – and this has been upheld by the courts… in Europe, too. Perhaps these rules could be enforced better. But we have them – and we have past Labour governments to thank in establishing much of the system now in place.

Labour governments did something else. Britain has an opt out of EU migration policies, but we opted into the so-called Dublin Regulation coming into force four months into Tony Blair’s first term. The Dublin deal is an EU-wide agreement on refugees: if anyone sets foot first in Greece or Italy and makes a claim for asylum in Britain later, he or she can be returned to the first EU country entered. This is a policy with wide support from across the political spectrum.

If Britain left the EU, we leave the Dublin deal altogether. We’re out and on our own. Britain could not return every asylum seeker to other EU countries as it would be outside the EU deal. This would increase the number of asylum cases heard – and supported – in the UK. It might also attract more cases to Britain as they would be considered here without possibility of return to other parts of the EU.

The UK is also a part of EU-wide intelligence on counterterrorism, as highlighted by Labour’s Shadow Immigration Minister and former DPP Keir Starmer. No doubt, the UK would remain a part of some shared system, but it might no longer be part of the same regulatory framework for tackling terrorists if outside EU system. This would inevitably raise issues over time about how intelligence can and should be shared with the UK as a non-member.

Vote Leave thinks we can take more control of Britain’s borders outside the EU and reduce net migration.

Yet the closer we look, migration would likely increase under the migration-promoting points-based policy of Australia; EU migration controls exist and ‘free’, uncontrolled movement does not; the UK could see more asylum seekers making their way to Britain without being returned to other EU countries entered first; and our EU-wide counterterrorism efforts would be needlessly complicated for no clear benefit to Britain or the EU.

Labour can make these points – and forcefully – as the engine behind much of the system and key agreements that made these controls possible. If the public wants better controls, we can do this better remaining in the EU – and thanks to the hard work of Labour governments.

While the Tories continue their civil war and David Cameron thinks his ‘deal’ more important than the public interest, it’s not too late for Remain to win the day. Labour supporters making a Labour-rooted case can make the difference.

Thom Brooks is Professor of Law and Government at Durham University’s Law School. His book Becoming British: UK Citizenship Examined is published by Biteback.