Jones has had a troubled relationship with the national tabloid press and they have often criticised him, his contribution to music, and his vocal abilities. Jones has generated headlines several times by criticising fellow Britpop and post-Britpop musical artists, most notably Radiohead frontman and solo artist Thom Yorke. Jones criticised Yorke's attitude in a 2002 interview due to what he felt was complaining about touring on Radiohead's 1998 home video release, Meeting People Is Easy. He said: "We can all relate to that video – y'know, having to do a hundred fucking idents for radio stations – but that doesn't mean you've got to walk around and be a miserable twat to everybody. Which is what Thom Yorke is mostly." He later expressed regret for this comment, since he was a fan of Yorke.
Jones and his first girlfriend were together for almost 12 years and had become engaged but split up. In 2002, Jones, drunk, vandalised the house and car of a friend because Jones had discovered the friend was courting his ex-girlfriend. Jones was arrested, but his friend did not press charges. Jones wrote the song "Rainbows and Pots of Gold" in response to the event. Jones and Rebecca Walters had two children, but they split shortly after the birth of the second child. Jones then married MTV journalist Jakki Healy, and they have two children.