It would not be an overstatement to say that the Arctic Monkeys are the biggest new band to hit Britain in some time. Actually, it would be a gross understatement. In January, the indie-rockers’ CD, Whatever People Say I Am, That’s What I’m Not, became the fastest-selling debut album in U.K. chart history. The same month the NME placed it at No. 4 in a list of the 100 Greatest British Albums Ever, 93 places ahead of Led Zeppelin IV.

The Monkeys’ meteoric rise is even the more remarkable for having been largely propelled by the Internet file-sharing of tracks which the band gave away at their early shows. When the quartet signed last year to independent label Domino they were already a genuine cult phenomenon, one whose debut single, “I Bet You Look Good On The Dancefloor,” also topped the charts in October.

“I think we could have been successful without the Internet, but it might have taken longer,” says drummer Matt Helders, 19. “It’s not just because the songs were on the internet. You’ve got to have something to back it up.” That something is a hook-heavy musical mix of the Clash, Oasis and the Libertines topped off by the lyrics of front man Alex Turner, who dissects contemporary British (low-) life with a fearless verve, rhyming, for example, “ringtones” with “Sherlock Holmes.”

Though their CD also name-checks British sitcom character Frank Spencer and the British slang for tracksuit pants (“tracky bottoms”), Turner isn’t worried that the collection, which hits stores here today (and is streaming on AOL Music), might be too, well, British, for American ears. “Maybe they won’t understand everything,” he says. “But I like loads of music that I don’t quite understand.”

Whether the 19-year-old singer could cope with becoming any more successful, however, seems more open to debate. “It is quite crazy,” Turner admits of the band’s fame in the U.K. “I do sometimes wonder what’s happened to my life. Maybe I’ll go off the rails. Never say never!”