It’s not Portsmouth or Dover where the Aquarius, the Lifeline and other rescue ships are attempting to dock. It’s not happening in Britain and Brexiters would argue that soon Britain won’t even be part of the political union that has to deal with them.

But Brexit does not alter our geography or international legal responsibilities of states towards refugees and migrants. As EU leaders meet in Brussels to discuss migration, it’s in Britain’s interest that the EU finds a solution and incumbent on Britain to do the right thing – on substance and rhetoric.

Record numbers of people are fleeing conflict and persecution. And record numbers are being allowed into relatively poor countries such as Bangladesh, Uganda and, most recently, Colombia. The idea that the richest parts of the world – Europe, the US – are about to be overwhelmed by a refugee horde is fiction. But reactive, fragmented, inhumane policy can cause political crisis and that is what must be tackled.

Out of the EU, Britain can’t contribute to the Europe-wide discussions about how best to do this. (Another reason for a people’s vote on the final deal.) But even out of Europe, Britain should do the right thing – and not just in respect of EU citizens in the UK.

First, refugee resettlement. According to the UN refugee agency, there are 1.2 million especially vulnerable refugees in need of resettlement in a third country, because the country they first fled to cannot meet their basic needs, such as medical treatment.

This organised and planned movement of refugees at an appropriate scale has long been a missing piece in the migration system of European countries, including Britain. The US, long the standard bearer on resettlement, has pulled up the welcome mat. Britain currently accepts just six refugees per parliamentary constituency per year. The International Rescue Committee argues that increasing that by around four-fold – the British share of European responsibility – is perfectly feasible.

Second, governments, including Britain, need a fast, yet thorough system for processing asylum claims. They also need to share responsibility: it is unfair and short-sighted to expect Italy, Greece and Spain to take sole responsibility for new arrivals, simply because of their Mediterranean coastlines. Those who qualify for protection need effective integration into their new homes. Those who do not need to be supported to return home safely.

Third, there’s an opportunity to set the standard for refugee integration in Europe. There is much to learn from decades of experience of integrating refugees in the US, including the importance of private sector partnerships to get refugees into work. In the US, refugees pay more in tax than they receive in benefits and have higher rates of business formation than the host population.

Finally, Britain has a continuing role in aid and diplomacy, where it has historic and ongoing strength, to deal with the root causes of the record flows of people, which are diplomatic and political, from Syria to South Sudan. Retreat from the world’s problems will not make them go away. That is the false allure of the isolationists and the nativists. Quite apart from the abandonment of responsibility such an approach presents, it won’t work in a connected world, where if governments are not in charge, bandits, militias and people smugglers will be.

The rescue ships may not dock in Britain’s ports but the people on board, many of them vulnerable and traumatised, and all of them with legal rights, are our shared responsibility. A planned, well-managed humane migration policy is right for the EU and it’s right for Britain.

David Miliband is president and CEO of the International Rescue Committee