Adeyemi Olanrewaju Goodman Ajibade was born a royal prince of the house of Ọ̀ràngún from Ìlá Òràngún, Osun State, in the south-west of Nigeria. He attended Abeokuta Grammar School, and later pursued studies in London, at Kennington College of Law and Commerce (1955), at The Actors' Workshop (1960), and from 1966 to 1968 at the London School of Film Technique (now the London Film School), where he was a contemporary of filmmaker Horace Ové (who has recalled that they were the only two black students in the school at the time).
From early in his stay in the UK, Ajibade acted in radio drama for the BBC African Service. As producer Fiona Ledger recalled in 2007: "It was back in 1960 that the late BBC producer John Stockbridge was asked by the Head of the African Service to devise some kind of drama for African listeners. He came up with a series, a soap opera set in London. No copy survives, but" Yemi Ajibade "took the role of a social worker, moving around England and settling quarrels."
Continuing to develop his acting career, he was hailed in 1963 as "one of the most promising actors from West Africa". Alongside performers who included Yulisa Amadu Maddy, Leslie Palmer, Eddie Tagoe, Karene Wallace, Basil Wanzira, and Elvania Zirimu, among others, Ajibade featured in a production of Lindsay Barrett's Blackblast! filmed in 1973 for a special edition of the BBC arts and entertainment programme Full House devoted to the work of West Indian writers, artists, musicians and film-makers.
Ajibade's acting portfolio would eventually encompass roles in television series such as Armchair Theatre (starring in 1963 in "The Chocolate Tree" by Andrew Sinclair, together with Earl Cameron and Peter McEnery), Danger Man (1965), Dixon of Dock Green (1968), Douglas Botting's The Black Safari (1972), The Fosters (1976), Prisoners of Conscience (1981), and Silent Witness (1996), and work on the stage – for instance, in "Plays Umbrella" at Riverside Studios in August 1980 (in association with Drum Arts Centre, London), and Nicholas Wright's plays One Fine Day (1980 at Riverside Studios) and The Custom of the Country (1983 at The Pit, Barbican Centre), and in Lorraine Hansberry's Les Blancs (Royal Exchange Theatre, 2001) – as well as film appearances including in Terence Fisher's The Devil Rides Out (1968), Monte Hellman's Shatter (1974), Hanif Kureshi's London Kills Me (1991), Skin (1995, written by Sarah Kane), Dirty Pretty Things (2002), Exorcist: The Beginning (2004) and Flawless with Demi Moore and Michael Caine (2007).
In 1966 Ajibade led a delegation of British, West Indian and African members to the World Festival of Black Arts in Dakar, Senegal, directing a production of Obi Egbuna's play Wind Versus Polygamy; at the 2nd World Black Arts Festival in Lagos in 1977 Ajibade was supervisor of Drama Events. In 1975 he was appointed as a tutor by the Inner London Education Authority, and he also became artistic director of the Keskidee Centre in north London, where he directed a production of Wole Soyinka's The Swamp Dwellers (13–23 March 1975)