British history isn’t just about dates and battles, kings and queens. It’s about people’s stories – and as a youngster from a Jewish background growing up in east London, I wanted to know how my family’s story fitted into the national picture.

What I learned was that my family history reflected the way generation after generation of people have moved to and from Britain over the centuries. Which is why I’m so excited that today the country can finally boast a national Migration Museum (though it does not yet have a permanent home).

I first made the case for a migration museum for Britain almost 15 years ago, an idea that stemmed from my time as Britain’s immigration minister, and from visiting similar museums in other parts of the world – notably Ellis Island in New York.

Britain has one of the best museum sectors in the world, but there is no cultural space devoted to conveying the importance of migration in the narrative of this country. It has always seemed a strange omission, as if there is a reluctance to acknowledge the integral role migration has played in the formation of Britain as we know it.

A major step towards filling this gap in Britain’s cultural landscape is today’s launch of the museum, just across the river from the Houses of Parliament.

Over the next year this institution, where I am chair of trustees, will stage a series of exhibitions and events exploring who we are and where we come from, providing a showcase for the permanent museum that we aspire to create.

And because migration is very much a national story, we are coordinating a Migration Museums Network, funded by Arts Council England, that will bring together museums and galleries across the country to share knowledge and best practice.

Barbara Roche (right) and Sophie Henderson, of the Migration Museum project, at the Southbank Centre’s Adopting Britain exhibition in 2015. Photograph: David Levene/The Guardian

We won’t lack material. Migration often tends to be cast in contemporary terms – as a late 20th century, post-second world war, post-EU expansion, or even post-Arab spring phenomenon. Nothing could be further from the truth. As Robert Winder, a Migration Museum trustee, wrote in his book Bloody Foreigners: The Story of Immigration to Britain: “Ever since the first Jute, the first Saxon, the first Roman and the first Dane leaped off their boats and planted their feet on British mud, we have been a [migrant] nation.”

This is not to suggest that Britain’s migration history is – or has ever been – linear or smooth. On the contrary, it is as complex as it is long, with generation after generation of new arrivals facing challenges, sometimes acceptance and sometimes hostility. And, of course, these arrivals have also had an impact on those already here. Britain’s emigration story is equally – if not even more – contested, tied up as it is with issues of race, inequality and empire.

There are international comparisons to be made. Countries in the so-called new world, such as Australia, Canada and the United States, tend to acknowledge their migration histories more readily – albeit versions that communities displaced by the arrival of European settlers often disagree with. It’s not mere coincidence that Australia, Canada and the United States all have well-established museums dedicated to migration.

However, this new world-old world dichotomy does not alone explain the absence of a British Migration Museum. A growing number of European nations – such as Denmark, Germany, Belgium and Ireland – have museums dedicated to migration. Even France, where it is arguably a more contentious issue than it is in the UK, has the Cité Nationale de l’Histoire de l’Immigration in Paris.

There are many possible reasons for our lack of engagement with our migration heritage, not least anxiety about opening up discussion and debate on a potentially charged and challenging topic. But what seems clear to me – and to so many people from across the political spectrum who have pledged their support – is that with migration at the centre of current debates around Brexit and identity, there has scarcely been a more important time to establish a national cultural institution exploring the central role that migration has played in shaping who we are.

The public discourse tends to focus on numbers. Yet all migrants are individuals, with hopes and dreams, anxieties and feelings, flaws and gifts. A permanent national migration museum will ultimately be a fitting venue to explore our history through our stories – personal stories, national stories, universal stories: all our stories.

There is a truth that Winder encapsulates: “We are all immigrants,” he says. “It simply depends how far back you go.”

• The Migration Museum is located at The Workshop, 26 Lambeth High Street, London SE1 7AG, Wednesday-Sunday 11am-5pm, admission free