The artist, aka Florence Welch, picked up 'Best Female' and 'Best Track' for her cover of 'You've Got The Love' at the music magazine's annual ceremony.
Take That made their first appearance at the event since Robbie Williams returned to the group in July, in order to collect the 'Hall Of Fame' award.
As the boyband, led by Gary Barlow, accepted the trophy, Williams told the crowd: "Very happy to be back - first day and we've won an award. I'd like to thank my boys. Extremely happy here. Looking forward to the next few years."
Britpop legends Suede, who also recently reformed, were given the 'Q Inspiration' award.
Lead singer Bret Anderson took the opportunity to recognise former guitarist Bernard Butler, saying: "I don't think we can accept this award without mentioning Bernard and that great work he did with us early on. This one's for Bernard too."
Other big winners at the show at London's Grosvenor House Hotel included producer Mark Ronson, who received the 'Innovation In Sound' award, folk rock act Mumford & Sons, who were named 'Best New Act', and Kasabian, who topped the 'Best Act In The World' category.