Harrison's first musical career began with an eleven-piece reggae band called Echo Base. Harrison had stated that he knew he wanted to be a musician from the moment he watched Top of the Pops, an English performance show, and that he always admired reggae giant Burning Spear. Echo Base were signed to the same label as fellow Birmingham band UB40 and, despite releasing an album, disbanded after disagreements.
After talking to Echo Base's manager, Harrison met and joined a band called The Fanatics, where he played alongside future friend Simon Fowler. He had replaced Caroline Bullock, who angrily responded by "outing" homosexual Fowler to British tabloid paper The Sun a few years later. After playing together for a while, The Fanatics too disbanded, along with another Birmingham rock band called The Boys.
After the disbanding of The Boys and the Fanatics, Fowler and Harrison were part of another, new, band called Ocean Colour Scene. This band featured Simon Fowler on lead vocals and acoustic guitar and Oscar Harrison on the drums, with the addition of lead electric guitar player Steve Cradock and bassist Damon Minchella.
Ocean Colour Scene were hugely successful in the Britpop era. They were signed with record label Phfftt, who were later bought out by larger label Phonogram, before signing with other labels such as Island Records and eventually creating their own label, Moseley Shoals Records.
Harrison played the drums with Ocean Colour Scene as they played with artists such as Oasis, Paul Weller and others. Harrison himself said that he looked up to The Who's drummer, Keith Moon
Harrison also played a lot of acoustic sessions, playing the piano,with vocalist Fowler singing and playing the guitar for songs such as Profit in Peace. Harrison composed an arranged all the parts of song Don't play, and when playing programmed the instruments onto a Korg synthesizer.
Harrison first sang lead vocals for Ocean Colour Scene on a cover of the Bob Andy song My Time.
In 2016, Harrison joined the lineup of The Beat with Ranking Roger playing drums.
Harrison was born to Issac and Susan Harrison. He is the eldest of the four children his parents have: Rose, Peter and Paul Harrison. Harrison currently resides with a girlfriend in Edgbaston. He has two sons, Leon (Who is now the drummer with Little Liam) and Damon Stephen Simon Isaac Harrison; the name Isaac is taken from Oscar's father, as well as a daughter, Cherelle.
Harrison said that his biggest ambition is to live on a house boat and is obsessed with gadgets. He is an Aston Villa football fan and a regular golfer.
Harrison's brother, Paul, is the landlord of The Woodman pub on Curzon Street (opposite Millennium Point), Birmingham.