Born in Greenwich, south London, he was brought up on the south coast of England. He went to Sussex University in 1966 to study mathematics. While there, he became active in student politics and became sabbatical secretary of the student union from 1968 to 1969. He was frequent contributor to the student television service In Camera and the campus newspaper Wine Press. He did not complete his degree.
Jackson's first job was as marketing officer for British Student Travel in London. He then took a job as marketing manager for National Travel. In 1975 he moved to Manchester to take up a job with North West Arts. This was the start of a long career in the arts world. In Manchester he made contact with the Campaign for Homosexual Equality (CHE) and became an active campaigner. This led to him becoming the national treasurer.
In 1978 he moved back to London to take up a job as Publicity Manager for Greater London Arts. He joined the London Monday Group of CHE. He also took on the role of administrator for the experimental theatre group Gay Sweatshop.
He was instrumental in the creation of one of the first gay television programmes, which was about the sacking of the British Home Stores worker Tony Whitehouse when it was discovered that he was gay. Barry Jackson and his friends picketed BHS which eventually caved in. Tony Whitehouse became the president of the Terrence Higgins Trust.
Barry Jackson was responsible for putting out the first record of the London Records founder and gay activist Colin Bell. This was a 500-issue of a version of Tom Robinson's Glad to be Gay, distributed on the short-lived CHE Records record label.
He changed his job in 1980 to become Public Relations Director for the Arts Council of Great Britain. From 1985 he became its Development Director. Also in 1980 he volunteered for the London Lesbian and Gay Switchboard. It was one of the many organisations for which he would become a fund raiser. In 1983 he helped to set up the UK's first national conference on AIDS, and also the National AIDS Manual publishing house, and the National AIDS Helpline. He was employed as Development Director for the University of Westminster from 1990 to 1993.
In 1991 his closest friend Mike Rhodes died in a motoring accident and he helped set up the Mike Rhodes Trust which makes an annual award to an individual who has 'contributed most to promoting an understanding of lesbian and gay life'. He was Corporate Affairs Director for the Committee of Vice-Chancellors and Principals from 1993 to 1999. He also became a European trustee of the Council for Advancement and Support for Education.
In 1994 he joined the board of the Actors Touring Company and became its chair a year later. In the late 1990s he became involved with the Gay Pride march and festival, and was part of the movement to make the London celebrations more like the Mardi Gras in Sydney. He was at the centre of the response to the bombing of the Admiral Duncan pub in Soho in April, 1999.
A few weeks before his death Jackson was diagnosed with leukaemia. He was then struck down with severe influenza and died of pneumonia at St Thomas's Hospital, London.