The zoot suits. The neatly pressed skirt suits with matching pillbox hats and sensible court shoes. The gloves, the handkerchiefs, the reinforced cardboard suitcases (also known as “grips”) and the fixed, toothy smiles.

More often than not, when people talk of the arrival of black people on British shores, the narrative includes some or indeed all of the above. They almost always mention the following, too: Tilbury docks, Essex, 22 June 1948; the Empire Windrush; the West Indies and calypso music. Sometimes, the storyteller might mention the fact that the ship’s passenger list held the names of 490 men and only two women (there was a stowaway, whose fare was paid for by a ship-wide whipround). The arrival of the Empire Windrush was an important event not only for much of West Indian life in this country, but for British society itself – without it, what would the UK look like today?

But while this story, retold every October for Black History Month, is a part of the rich history of black people in the UK, it is by no means the whole story. There has been a black presence in the UK since the construction of Hadrian’s Wall (which began in AD 122) – a fact long overlooked.

Now the organisers of an exhibition at the recently opened Black Cultural Archives (in Windrush Square in Brixton, south London) are hoping to skewer some myths regarding black life in the British Isles. The archives’ inaugural exhibition, Re-imagine: Black Women in Britain, has brought together a number of black women who made the country their home over the centuries. The stories of these women and their contributions to British life are a necessary corrective to the idea that we are somehow “new” to Britain. Consider Mary Prince, an enslaved woman from Bermuda – whose personal account of slavery was published in 1831, and was the first account of the life of a black woman in Britain. “I have been a slave myself,” she wrote. “The man that says slaves be quite happy in slavery – that they don’t want to be free – that man is either ignorant or a lying person. I never heard a slave say so.” She eventually lived and worked at the home of the Scottish writer Thomas Pringle, secretary of the Anti-Slavery Society.

Adelaide Hall, who in 1941 became Britain’s highest-paid female entertainer. Photograph: Museum of the City of New York/Archive Photos/Getty

The exhibition features some well-known women: Crimean war nurse Mary Seacole, entertainer Adelaide Hall (who in 1941 replaced Gracie Fields as Britain’s highest-paid female entertainer) and justice campaigner Lady Lawrence among them. But it also has non-household names and stories. From slavery to the upper echelons of English society, across the naval service and the entertainment industry and in social and political activism, these women have left their mark.

Dr Suzanne Scafe, reader in Caribbean and postcolonial literature at London South Bank University has published several essays on black British women’s autobiographical writing. She suggests that the exhibition should act as a trigger for the visitor: the aim is to pique interest that will inspire further digging. “It prompts you to think about other stories,” she says. “I think no exhibition can be fully comprehensive. The purpose is really just to make a statement of our presence. It is important for people to recognise that Britain has always been a mixed society, that black women have always played a role in this society. I think it does that.”

A few of the women who could use a higher profile are the activist and publisher Jessica Huntley, who was also involved in the Black Parents Movement, and Claudia Jones, often described as the mother of the Notting Hill Carnival. There’s also the story of Seaman William Brown, which all but cries out for a film to be made: she was the first black woman to serve in the Royal Navy (the Annual Register 1815 remarked that “her features are rather handsome for a black”).

One of the women who left a huge legacy is Olive Morris, a Lambeth-based community organiser and activist whose name remains stubbornly unknown. She was born in Jamaica in 1952 and died in 1979, but in her short years achieved a staggering amount: she co-founded the Organisation of Women of African and Asian Descent and the Brixton Black Women’s Group. By the time she died of a non-Hodgkin lymphoma at the age of 27, she had also helped set up, in the city where she went to university, the Manchester Black Women’s Co-operative and the Brixton Law Centre, and was active in the Black Panther movement, too. One story tells of a 17-year-old Olive stepping into the fray after police stopped and searched a black man they suspected of stealing a Mercedes (he was a Nigerian diplomat who had stopped to do some shopping). She was beaten and arrested. By all accounts she was fearless – and committed to changing Britain for the better.

Seven years after her death, Lambeth council honoured Morris by naming a building after her (it is now a Brixton customer centre, where residents can make inquiries about council tax and benefits). She has also been commemorated in currency – an image of her, talking into a loudspeaker, is on the Brixton pound note. It’s time more people heard of her – and the other unsung foremothers in Black British history.

• Re-Imagine: Black Women in Britain is at Black Cultural Archives, London SW2, until 30 November