While collecting the award, Roxy Music frontman Bryan Ferry expressed support for his pro-hunt protester son, Otis.
The 21-year-old invaded the House of Commons with four friends last month in protest over the government's bill to ban fox-hunting.
"I would like to dedicate this award to my brave son
Otis," said Ferry, whose speech was met with muffled boos.
Keane's Hopes and Fears was named best album, Franz Ferdinand's Take Me Out won the best video prize and Razorlight were named best new act.
Triple Mobo winner Jamelia took home the best single award for See It In A Boy's Eyes, written with Coldplay's Chris Martin.
The Grosvenor House Hotel music magazine event was attended by musicians including U2, the Pet Shop Boys and Elvis Costello.
Sir Elton's outburst came after he branded Taiwanese photographers "rude,
vile pigs" at an airport last month.
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Q Award winners 2004:
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Best new act - Razorlight
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Best producer - Mick Jones (for the Libertines)
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Best live act - Muse
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Best video - Franz Ferdinand (Take Me Out)
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Q Merit Award - Shane McGowan
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Best single - Jamelia (See It In A Boy's Eyes)
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Q Innovation and Sound Award - Human League
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Q Inspiration Award - Pet Shop Boys
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Best Album - Keane (Hopes and Fears)
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Best Act in the World Today - Red Hot Chili Peppers
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Q Classic Songwriter award - Sir Elton John
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Q Icon Award - U2
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Q Lifetime Achievement Award - Roxy Music