Sam King MBE sailed to the UK on the Empire Windrush in 1948 and was elected as Mayor of Southwark in 1983.
A war veteran, he was also a driving force behind Britain’s first black newspaper, the West Indian Gazette.
Dione McDonald said the 90-year-old had been unwell in recent months and had passed away with his family around him.
Born in 1926, Sam King first came to Britain after volunteering for the Royal Air Force as an engineer in 1944, after spotting an advert in the local paper.
In an interview last year, he said he had “left Portland, Jamaica, in temperatures of 75F (23C).” When he arrived in Britain the temperature was 39F (4C): “I thought I was going to die.”
After returning to Britain on the MV Windrush and settling in Southwark, he found work as a postman and became an active campaigner in the community.
In the mid-1950s he became circulation manager of the Brixton-based Gazette.
He later helped organise the first Caribbean-style carnival in London which later became the first Notting Hill Carnival in 1964.
Tributes have been paid to Mr King with many calling him a “pioneer” in British politics.
Speaking to BBC Radio London, Labour MP Diane Abbott said Mr King was a “very dignified and very gentlemanly” person who helped break down barriers for black people in politics.
“Someone like myself who was fortunate to become an MP stands on the shoulders of people like Sam King,” she said.
Southwark Councillor Michael Situ tweeted that the World War Two veteran was “principled, inspiring and always willing to serve”.