Last week, however, Mills admitted, in a detailed four-page-long fax, that he had indeed dabbled with Nazism and its most potent symbol, the swastika.
Clues to his opinions had already appeared in recent interviews with the specialist music press. "I'd LOVE to have great big flaming swastikas onstage just for the f-- - of it," he told the New Musical Express in its 1 March edition.
Mills' lengthy explanation and apology, faxed to the Independent on Sunday from the United States where he is on a 30-date tour, highlights his interest in the swastika. "This has justifiably upset many people for which I am deeply sorry," he said. "There is no better example of my naivety and insensitivity than the swastika comments."
Mills went on to defend his views by explaining that he was referring to the swastika as an ancient Indian spiritual symbol rather than the Nazi emblem.
But Mills has not commented on the swastika alone during interviews. "Hitler knew a lot more than he made out," Mills said in the New Musical Express interview. "You can see why Hitler got support. It was probably the uniforms that swung it," he told the same publication in November 1996. "Well, we know that democracy doesn't work. If we had a non-elected body that set the right standards ..." he explained to Melody Maker in January 1997.
His outspokenness has coincided with remarkable success for Kula Shaker: five hit singles, a million-selling debut album and the best-newcomer prize at the Brit Awards, has enabled them to challenge Oasis and Blur as Britain's top group.
Five years ago, Mills was unknown. He and Marcus Mac-laine, who was the partner of Mills's actress mother Hayley for 12 years, had formed a band called The Objects of Desire. According to Maclaine, they gave it the motto "England will rise again". The group did the usual round of clubs and backstreet venues making a limited impact on the music scene.
But in 1993 the band was lined up to play a far bigger gig at Wembley: a conference entitled "Global Deception" at which speakers included a notorious anti-semitic propagandist Eustace Mullins and a leading US militia writer, William Cooper.
Cooper, who stepped in as compere at the conference after the right-wing, militia-supporting DJ Anthony J Hilder failed to appear, has reprinted the anti-semitic forgery, the Protocols of the Elders of Zion, which was used by the Nazis to justify the Holocaust. Mills later went on to thank Cooper on Kula Shaker's hit album K, which reached number one in the album charts in September last year.
Maclaine was no stranger to extremist politics himself, having spent time in the National Front as a teenager, although he says he has had nothing to do with the organisation since he was 18.
He and Mills fell out after the singer quit The Objects of Desire, taking Paul Winter-Hart and Alonza Bevan with him to form Kula Shaker.
Mills' unguarded remarks are in stark contrast to his mother's image as the star of wholesome films such as Pollyanna and Whistle Down The Wind. Hayley Mills, who is also on tour in the United States, in her case performing in the musical The King and I, refused to comment, as did his grandfather, Sir John Mills, whose roles in Second World War movies were the embodiment of British pluck in the face of Nazism.
Kula Shaker's flirtation with the far right was first uncovered during a probe into "New Age Nazism" - a cross-fertilisation of extremist politics with spirituality - by the small investigative political magazine Open Eye.
John Murray, co-editor of Open Eye, said: "The symbols and texts of fascism were consigned to history after the horrors of the Second World War, but now there is a disturbing cultural trend towards resurrecting them which Kula Shaker seems to have become part of."
Matt Snow, editor of the music magazine Mojo, believes Kula Shaker has the drive and ambition to be Britain's top rock act. But, he said, Mills' "delight in image has certainly backfired in this instance over the swastikas".