At the age of 16, Kennedy was invited by leading jazz violinist Stéphane Grappelli to appear with him at New York’s Carnegie Hall. He made his recording debut in 1984 with Elgar’s Violin Concerto. His subsequent recording of Vivaldi’s The Four Seasons with the English Chamber Orchestra in 1989 sold over two million copies and earned a place as one of the best-selling classical recordings ever. The album remained at the top of the UK classical charts for over a year, with total sales of over three million units.

Kennedy was romantically involved with singer/guitarist Brix Smith after she had broken up and divorced husband Mark E. Smith in 1989. Kennedy currently divides his time among residences in Malvern, Worcestershire (where his former girlfriend Eve Westmore and son Sark Yves Amadeus b.1997 reside), London and Kraków, Poland. He has been married twice; his second wife, Agnieszka née Chowniec, is a Polish actor and artistic director, born in April 1977.

Kennedy published his autobiography, Always Playing, in 1991. He then withdrew completely from public performance, at which point he made the album Music in Colours with Stephen Duffy. He returned to the international concert platform five years later. In 1997, he received an award for Outstanding Contribution to British Music at the BRIT Awards, and in 2001 received the ‘Male Artist of the Year’ award.

In 1991, he was awarded an honorary degree (Doctor of Letters, or Litt.D.) by the University of Bath.

In 1991 John Drummond criticised Kennedy publicly, calling him “a Liberace for the nineties” and noting specifically his “ludicrous” clothes and “self-invented accent”.

In other music genres, Kennedy recorded a cover of Jimi Hendrix’s “Fire” for the 1993 album Stone Free: A Tribute to Jimi Hendrix. The same year, he made an appearance on Robert Plant’s solo album Fate of Nations on the track “Calling to you”. In 1999, Sony Classical released The Kennedy Experience, which featured improvisational recordings based on Hendrix compositions. In 2000, he recorded Riders on the Storm: The Doors Concerto (with Jaz Coleman), a violin-based orchestral version of Doors songs, including “Strange Days”, “LA Woman”, “The End”, and “Riders on the Storm”. On 27 November 2000, Kennedy joined rock group The Who at the Royal Albert Hall to play the violin solo in the song “Baba O’Riley”, released three years later on the album Live at the Royal Albert Hall. Kennedy also played on several tracks – notably “Experiment IV” – by British singer-songwriter Kate Bush, who was a guest on Kennedy’s episode of This Is Your Life. He was featured on two of Sarah Brightman’s songs for her 2003 album Harem. He has explored Klezmer music with the Polish jazz band Kroke. In late 2005, Kennedy recorded his first album for the jazz label Blue Note Sessions, with Ron Carter on double bass, Jack DeJohnette on drums and saxophonist Joe Lovano.

Until 2006, Kennedy expressed his intention of not appearing on the classical London concert scene with a London orchestra, which was seen by some as arrogance, although he rationalised it in terms of frustrated perfectionism:

In 2013, the BBC censored the violinist’s attribution of apartheid to Israel, which had been made during a Proms performance, from its broadcast of the event. Kennedy registered his objection to the removal of his remarks from the telecast, during which he had said,