Amma Asante is perched on a sofa in London's Soho Hotel, wearing heels, gold jewellery and a full-length floral dress. The day before her new film A United Kingdom opens the London Film Festival, the 'butterflies in the stomach are starting', she says, and it's no wonder. With just her third film, following on from 2013's well-received 18th-century drama Belle, the striking-looking 47 year-old is the first black filmmaker ever to open or close the LFF. 'It feels massive,' she says, quite rightly.

Arriving in the year when debates about diversity in the film industry led to the #OscarSoWhite campaign across social media platforms, Asante's movie couldn't be better timed. A story of a real-life interracial relationship, it begins in 1947 – where London clerk Ruth Williams (Gone Girl star Rosamund Pike) falls in love with the African-born Seretse Khama (Selma's David Oyelowo) while he's in England studying law.

Of noble blood, Seretse was in fact set to become ruler of Bechuanaland – or Botswana, as it would become when it finally gained independence from Britain in 1966. But when he and Ruth marry, this dignified leader becomes the subject of political brinksmanship – with the British government desperate to keep the couple apart or lose the favour of Bechuanaland's neighbour, the mineral-rich South Africa, with its newly implemented apartheid regime.

Asante first came across the story from Guy Hibbert's script – adapted from the book Colour Bar: The Triumph of Seretse Khama and His Nation by Susan Williams. Stirring up 'so many feelings', she says, 'it was not lost on me how audacious Seretse was in wanting to take a white queen back to Africa and back to the black women of his nation. But there was anger and frustration [I felt] as well – that one country could separate a man from another country.'

A former child actress (including Grange Hill), Asante became a screenwriter in her early twenties, developing the show Brothers & Sisters, long before she made her directorial debut with 2004's A Way of Life. But it was her own bi-cultural background that tuned her into Seretse and Ruth's story. Both her parents are from Ghana, and came to Britain in the late 1950s – her father working as an accountant, her mother running a delicatessen.

The very fact that Ghana was the first sub-Saharan country in Africa to gain its independence was not forgotten in her household. 'Many families have a picture of the Queen; we had a picture of the Ghanaian president [on the wall],' she recalls. 'So I do think it's interesting … that this story that I'm telling in many ways [was] informed personally for me by the stories my father used to tell me – about living in a colony, about Independence Day in Ghana.'

The resonances extend far beyond Asante's own upbringing, however. While A United Kingdom has been a mooted project for over six years, its title feels somewhat provocative in these post-Brexit times. 'I loved the irony that actually we're not talking about Britain,' she laughs. True enough – the title obviously refers to Seretse's Bechuanaland, rather than the currently divided UK – but there's no question the film has contemporary meaning. 'Reflecting [on the past] sometimes has a really major impact on now,' she says, 'and what we do going forward.'

According to Asante, there's 'something in the air' and it's not just Britain that's facing instability. 'If you think about America, it's just coming out of a period where it's had its first black President. It might be about to go into a time where it has its first female President. We are now, after all these years, sitting in a period where we have only our second female Prime Minister. We've just voted for Brexit. These are highly politicised times. And I do think as filmmakers it's our job to reflect the times we're in.'

Then there's that perennial question of diversity. With the British Film Institute about to kick off Black Star, a three-month long season of black-themed movies, Asante admits that things are changing in the film industry – albeit slowly. 'I definitely think we're getting to a time where we're becoming more comfortable with people of colour being at the centre of their own stories. They're not being bystanders or the supporting artists, but being at the centre of their own narrative.'

Asante is next lining up Where Hands Touch – a romantic drama set in 1944 Berlin about a mixed-race German girl and an SS Officer. She makes no apologies that it's another period piece – well-aware that she's not in a position to fully dictate her choices after just three movies. 'I still have some stripes to earn in many ways.'

But, she hopes, black filmmaking isn't going to be restricted to true-life period tales. 'Who knows?' she says, 'one day [maybe we'll see] a futuristic story with an all black cast.'

A United Kingdom opens on Fri 25 Nov.