The study, by music industry research company The Leading Question, revealed that regular downloaders of illegal music spend an average of £5.52 on legal music whereas other music fans spend an average of £1.27.
Paul Brindley, director of The Leading Question, said: "Research clearly shows that music fans who break piracy laws are highly valuable customers.
"There's a myth that all illegal downloaders are mercenaries hell-bent on breaking the law in pursuit of free music. In reality, hardcore fans 'are extremely enthusiastic' about paid-for services, as long as they are suitably compelling."
The research also suggests that instead of taking legal action against illegal downloaders, the music industry should work harder to entice consumers to use legal alternatives.
Music trade body, the British Phonographic Industry, has secured settlements worth several thousands of pounds from more than 90 people, who have been caught sharing illegally downloaded tracks over the internet from file-sharing sites like Limewire and BitTorrent.
BPI spokesman Matt Philips said: "It's encouraging that many illegal file sharers are starting to use legal services."
Since internet music downloads first surfaced in 1999, music sales have fallen by 25%, with record companies giants such as EMI and Sony BMG attributing the fall to illegal music downloads.
The Leading Question research follows another recent report by the International Federation of Phonographic Industries, which said that the growth of legitimate downloads was being pushed by the threat of lawsuits. It said 180m tracks had been downloaded globally between January and the end of June.
Downloads are now included in the official charts and has had the affect of keeping singles in the charts for longer, most recently seen with James Blunt and his single 'You're Beautiful', which had a seven-week climb to the number one spot rather than entering high and then quickly falling out.
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