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Baker, who was born in south London in 1939, first came to prominence as a member of blues group The Graham Bond Organisation before founding Cream in 1966.
The band released four groundbreaking albums that brought together blues, psychedelic rock and hard rock before disbanding in 1968.
Baker went on to work with Nigerian Afrobeat pioneer Fela Kuti and joined English rock band Hawkwind for a period in the 1980s.
Baker's family said last month he was critically ill in hospital.
"We are very sad to say that Ginger has passed away peacefully in hospital this morning," a notice on Baker's Twitter feed said on Sunday.