Actually, the
Second British Invasion was the 80s: Duran Duran, The Human League, ABC, A Flock of Seagulls, Thompson Twins, Wham!, Eurythmics, Culture Club, Depeche Mode, The Cure, Siouxsie, Madness, Bananarama, etc.
I have no idea what you're talking about with your
"second british invasion". The Chemical Brothers, The Prodigy, and Fatboy Slim were certainly popular with the dance club\electronica crowd, but barely made a blip in the music scene here otherwise. To people outside those relatively small genres, Chemical Brothers are "that band I once heard on college radio", The Prodigy are "That 'Firestarter" band... oh, and didn't they have that one song that made N.O.W. mad?" ("Fatboy Slim... wasn't that one of Eminem's early personas?")
To show you how much British music had fallen in the US, James Blunt's "You're Beautiful" (2006) was the first British artist of any kind (male, female, band, etc.) to have a #1 single in the US in almost 10 years (Elton John's "Candle in the Wind" was #1 in 1997; one wonders what the time span might have been if not for Diana's accident). Leona Lewis's 2008 single "Bleeding Love" was the first single by a British woman to hit #1 in the US since 1986.
Brit music is making a comeback though. Lewis, Lilly Allen, Amy Winehouse, Coldplay, Natasha Bedingfield and Snow Patrol are doing well, and it seems like rock music is slowly making a comeback against hip-hop, which also bodes well for British artists.