As Europe’s leaders gather on Wednesday for an emergency summit on the worst refugee crisis since the second world war, it may seem as if the disarray is a good reason for Britain to leave the European Union. The wave of asylum seekers fleeing war in the Middle East has certainly played into the hands of Eurosceptics, who argue that quitting the EU is the only way for Britain to take back control of its borders.

Nigel Farage said on Twitter on 17 September: “Border chaos across Europe is making immigration issue even more of a concern for the British people than ever before. Choice is clear: either we vote to leave the EU & start controlling immigration sensibly or we have EU open borders.” The Know, one of the groups campaigning for Britain to leave the EU, says the reason so many people have registered on its website may be because “the migration crisis has woken people up”.

But the argument that we should leave the EU because of the refugee crisis is riddled with flaws. For a start, we never gave up control of our borders in the first place. We didn’t sign the Schengen agreement, which removed border controls between 22 EU countries and four other non-EU countries.

So when asylum seekers or economic migrants get into the EU, they cannot just hop on a bus or a train and come to the UK. They get stopped at our border and can be denied entry if they don’t have a visa. This makes us very different from countries such as Germany, Croatia and Austria, which are frantically reimposing border controls to stem the flood of people entering their countries.

In fact, if we left the EU, we would find it harder to manage the flow of migrants and asylum seekers because we would no longer be covered by its Dublin regulation. This specifies that the country where asylum seekers arrive has to process their applications. If it grants them asylum, it is responsible for looking after them. The refugees are not free to travel where they like. But if they do end up somewhere else in the EU, that country can then send them back to the country where they first sought asylum. We’ve already sent back 12,000 since the rule came into effect in 2003.

The Dublin regulation is especially useful for a British government that wants to limit the flow of asylum seekers, because we are near the end of a route that starts in the Middle East and crosses into Turkey, Greece and then the Balkans, before it arrives in northern Europe and ends at Calais.

Far fewer asylum seekers reach here than arrive in countries closer to the source of the problem. And if they do get to Calais and want to come to Britain, the French authorities have to try to stop them.

If we left the EU, we would no longer be able to rely on the cooperation of the French. Our border with France would effectively shift from Calais to Dover. And when asylum seekers did arrive, we wouldn’t have any right to send them back – that is, unless we pleaded with the EU to let us stay covered by the Dublin regulation, and it agreed.

We have also opted out of most of the EU’s policies on justice and home affairs. This means we cannot be forced to take refugees from other countries such as Greece and Italy. That’s why David Cameron can refuse to take part in a scheme to spread refugees more evenly across Europe, which will be discussed at Wednesday’s summit. Britain does, of course, have a moral duty to help. Cameron agreed to take 20,000 Syrian refugees over the next five years after realising that his initial heartlessness was not going down well with the British people.

What’s more, by staying in the EU, we attend summits and council meetings that can solve other aspects of the refugee problem. We get a vote on how to manage asylum seekers when they arrive in the EU.

We were, for example, at last week’s EU council meeting that provisionally decided on stronger measures so asylum seekers really do stay in the first country where they arrive. We were at the table when the rest of the EU discussed beefing up policing of the Schengen area’s vast external border with Turkey. Even though we don’t vote on such matters, we can give our view, and have provided ships to help Frontex, the Schengen countries’ border agency.

The same meeting also provisionally agreed to provide more money to help refugees in frontline states such as Turkey, Lebanon and Jordan – the idea being that fewer will then come to the EU. Again, Britain was part of the decision-making process. We also provide our own aid to frontline states. But we have extra impact by working simultaneously with 27 other countries.

Finally, we will have more chance of contributing to peace in Syria, Libya and Iraq – which is the only real solution to the refugee crisis – if we work with our EU partners. Of course, we need to work with the UN and America too. But this is Europe’s backyard. Our influence would be reduced if we quit the EU.

In other words, Britain has the best of all worlds: the protection of the Dublin regulation and a seat at the table when decisions about Europe’s asylum policy are taken without being exposed to Schengen’s open borders or having to participate in schemes to relocate refugees. The crisis, far from being a reason to quit the EU, is a reason to get stuck in.