Damian Green is a former Immigration and Policing Minister, and is MP for Ashford.

In the wake of last week’s shocking events in Brussels, Brexit campaigners have stepped up their rhetoric to argue that these attacks demonstrate that we would be safer outside of the EU. Irrespective of the unfortunate speed with which political capital was sought, these are actually very important arguments that demand proper consideration. As we have sadly seen, these are literally matters of life and death – so claims that there may be ways to prevent future attacks in Britain should be taken seriously and examined forensically.

If it is true that leaving the EU would make murder and terror in Britain less likely, that would be an enormously important consideration for voters. It would change minds, and rightly so. But if it isn’t true, and these arguments are based on lazy misunderstandings – or even untruths – then it amount to dangerous scaremongering that voters should rightly dismiss. Worse, if there is a risk that leaving the EU would actually make the British people less safe, then they deserve to know that before they make their choice.

So let’s look at the arguments. The first is that we need to leave to reclaim our borders and prevent terrorists coming into our country. It isn’t just Nigel Farage who says this; serious politicians do, too. Our “open border”, Iain Duncan-Smith claimed last month, means that we “leave the door open” for terrorists to come to the UK.  Even last week, my friend and colleague Chris Grayling said that “we want to know who is coming to and from the country, and it’s nonsense that European rules have prevented us from doing that.”

But this just isn’t right. These claims are based on a huge misunderstanding of what ‘free movement’ means. It means the freedom to move around Europe to take up a job, not the freedom to enter any country you like. Don’t believe me? Here are the facts: the UK checks the passport details of every single person who comes into our country, including EU nationals. They are checked against terrorist watch-lists and other alert systems, and we regularly stop people – including EU nationals – at our border and deny them entry. Since 2010, we’ve turned away 6,000 EU nationals because of security concerns, as well as tens of thousands of non-EU nationals. Does that sound like an open border to you?

The truth is that because we are not part of Schengen, we have a hard border (aided, of course, by hundreds of miles of open sea), with increasingly sophisticated EU cooperation to help us identify those who we shouldn’t let in. If we left, that cooperation would be harder, and we’d actually risk allowing in people who threaten our security. So it is complete rubbish to claim that leaving the EU would allow us to reclaim our borders; they are already completely within our control. Indeed, we even have border controls in France that prevent many, many illegal migrants from ever reaching our shores at all. And these would be put at risk if we left the EU. When you have jihadis apparently posing as refugees, I have to ask those who argue for Brexit: how on earth would a migrant jungle in Kent make us safer?

The second, more serious argument has been put forward by Sir Richard Dearlove, a former head of MI6. This is the idea that European cooperation on security adds little to our capabilities, and any activities or data sharing that we do find useful could be easily continued following Brexit. Of course, Sir Richard is right that our cooperation with the USA and our other ‘Five Eyes’ partners is the foundation stone of our intelligence cooperation.

However, I am afraid that his reasoning contains basic errors. He is wrong to say that Brexit would mean we could leave the European Court of Human Rights. These are two completely separate institutions. And he is wrong to say the European Arrest Warrant is used for “exclusively criminal” purposes and is therefore irrelevant to terrorism: we actually used this mechanism to bring back and prosecute one of the failed 21/7 bombers who had fled to continental Europe.

But above all, Sir Richard is simply wrong that EU cooperation is “of little consequence”. Since he left his post in 2004, the world has changed and so has the EU. The Europe-wide Counter-Terrorism Group – to which Sir Richard referred today as slow and leaky – is today a very important forum, and increasingly useful on intelligence sharing.

And look at what is happening at an EU level today. We need to work together inside the EU to control the flow of firearms – and we are, with Britain in the lead. We need to strengthen aviation security, including with access for European countries to passenger name records, and it is only thanks to our position inside the EU that we have been able to drive this debate. And we need to develop a fully-functioning warnings index and intelligence sharing system – and we will, with new capabilities introduced to provide alerts, in real-time, across Europe.

We wouldn’t just miss out on this new cooperation if we left; we’d also lose access to the influence we have over existing arrangements today. Our Prime Minister, Home Secretary and senior security officials wouldn’t be in the rooms where decisions were made on these issues in future. Brexit would mean an instant and irreversible loss of British influence on decisions affecting our national security.  Why else do you think, contrary to Sir Richard’s view, that our most important ally, the United States, is so keen for us to stay inside this organisation?

Don’t take my word for the growing importance of the EU to our security: Britain’s intelligence agencies, who we charge with keeping us safe, see this closer cooperation as absolutely vital for Britain’s security. They demand it. Ask yourself: are they all wrong, and the Leavers right?  After Paris and now Brussels, it’s absolutely right that we have a debate about our national security. But as we do so, let’s avoid claims based on gut feelings, out-dated information or – dare I say it – wilful misunderstandings.   And let’s instead focuson the real, practical measures needed to keep the British people safe.