Many who had travelled from the Caribbean to help rebuild post-war Britain attended the commemoration to mark the moment hundreds disembarked from the ship Empire Windrush at Tilbury Docks on June 22, 1948.
The Prime Minister clapped along, smiling and swaying, as a gospel choir sang Jesus Hold My Hand, while actors recounted the story as though they had just stepped off the ship.
Mrs May was joined by Home Secretary Sajid Javid, London mayor Sadiq Khan and shadow home secretary Diane Abbott, as well as Baroness Lawrence, the mother of murdered black teenager Stephen Lawrence.
Baroness Floella Benjamin, Lib Dem peer and patron of the Windrush Foundation, briefly danced in the nave of the Abbey to music on steel drums.
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She was joined in the congregation by Andria Marsh, 63, who proudly displayed pictures of her parents and her original British passport after the service.
The Rev Canon Joel Edwards said the Windrush generation had provided Britain with trade union leaders, politicians and senior civil servants. But he said many who left the Caribbean for a new life here faced hardships, including racism, as he paid tribute to “Windrush resilience”.
The Government has been criticised over a scandal that has seen some of those invited here decades ago facing deportation.
The Home Office said more than 2,000 people have been provided with documentation since April by a dedicated Windrush task force, helping them demonstrate their right to residence.