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The 37-year-old British funnyman met Peck, 25, at Sydney's ARIA Music Awards, and the good times continued, The Sun said.
"They've been enjoying quite a passionate fling, mostly at the swanky Park Hyatt," an unnamed source told tabloid.
"They've seen each other a few times. Kate likes his cheekiness, he's definitely her type. Unlike former girlfriends, Russell wanted to keep it all top secret."
Brand has been linked to a number of women - including fellow Briton and Spice Girl Geri Halliwell, 40, since his divorce from singer Katy Perry in December 2011.