The latest data shows that Black African, Black Caribbean, and...
More than 2,000 people gathered for a service at Westminster Abbey to mark the anniversary.
Hymns including Amazing Grace were played on steel drums as the guests made their way into the church.
The Rev Canon Joel Edwards, addressing a congregation including members of the Windrush generation and their descendants, hailed the positive impact those who landed at Tilbury Docks on June 22 1948 and their offspring have had in the worlds of politics, business, music and food.
He said the Windrush generation had "gifted Britain", providing trade union leaders, politicians and senior civil servants, as well as becoming leaders in various other areas of British life.
But many of those who left sunnier climes in the Caribbean for a new life in Britain faced hardships including racism, Mr Edwards said, as he paid tribute to "Windrush resilience".
He said: "Settling down hasn't been plain sailing. The children of Windrush have experienced over-representation in Britain's prisons and mental health institutions. Knife crimes.
The Liberal Democrat peer, Baroness Floella Benjamin was applauded as she briefly danced in the nave to the music.
As the patron of the Windrush Foundation she said afterwards that she felt "joy", adding: "I was floating, like a bird, free."
Other guests included Prime Minister Theresa May, Home Secretary Sajid Javid, London Mayor Sadiq Khan and Baroness Doreen Lawrence - mother of murdered black teenager Stephen Lawrence.
The government were recently heavily criticised for making life difficult for the windrush generation, leading to Amber Rudd's resignation as Home Secretary.
A Home Office spokesperson said: "The Home Secretary has apologised unreservedly for the distress caused to people of the Windrush generation. These are people who have contributed to the UK over a number of decades and it is our priority to ensure that those who have struggled to demonstrate their right to be here are supported to do so.
In the service, actors recounted the story of those who left their native islands to make the long journey to Britain, showing both the joys and hardships faced by immigrants.
Mrs May clapped, smiled and swayed as a gospel choir, wearing the red, green and yellow of the Caribbean, sang.
A Christian councillor and therapist told Premier the efforts of Caribbean migrants who arrived in the UK to help rebuild post-war Britain 70 years ago needs to be emphasised.
Commenting on the contribution Caribbean and black people have made to the country, Angela McDonald said: “The arrival of the Windrush isn’t the beginning of course; black people have been in Britain for over 400 years and 15,000 people fort in the Second World War. We were asked to come and help in the war effort and we did.
“So we continue to contribute within the NHS, nurses and porters, on the public transport.”
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