In the video for “Love Me or Hate Me,” the first single from Lady Sovereign’s American debut album “Public Warning,” Tetris blocks come together to form her pint-sized picture again and again. It’s a good metaphor for the 5-foot-1-inch British rapper and purveyor of grime, the British rap offshoot she represents: The pieces may finally be falling into place.

“Public Warning”will be released on October 31 by Def Jam, with the full-throated endorsement of its celebrity brass. (Lady Sovereign auditioned in person for Jay-Z, L.A. Reid, and Usher). “Love Me or Hate Me” is featured in the new Verizon Wireless ad campaign for its MP3 cellphone, and, most improbably, the video reached number one on MTV’s Total Request Live last week, beating out the likes of the Killers, T.I., and Justin Timberlake.

Such a breakthrough has been a long time coming for grime. It’s been almost three years since Dizzee Rascal, the genre’s first ambassador, made his debut on these shores.”Boy in Da Corner,”with its depth-charge beats and cubist rhymes, won the coveted Mercury Prize and unanimous raves from the American press. Yet it failed to find an American audience of any size.

Lady Sovereign’s early success is especially impressive when you consider that she’s done it on her own terms. There are no star cameos or super-producers on the album; a remix of “Love Me or Hate Me” featuring Missy Elliot was left off the final track list, and a session with the Neptunes yielded nothing. Instead, she has stuck with the horse that got her here: the grime-y sounds (especially on “Tango” and “A Little Bit of Shhh”) of her hometown producer, Medysn.

But the real secret of her near-success isn’t her foreignness, it’s her familiarity. Lady Sovereign bears a strong resemblance to a certain peroxide-blond American rapper. “People want to classify me as an Eminem / what hear what, I’m a different kind of specimen,” she insists on a hater-bashing song “Blah Blah.”

Despite her protestations, the two have much in common. Like Eminem, Lady Sovereign is a comic brat with a potty mouth and a razor tongue. She shares Eminem’s juvenile fondness for bathroom humor, and Jay-Z is the Dr. Dre to her Eminem, giving Lady Sovereign instant credibility with the American hip-hop market.

Most important, she has mastered Eminem’s trick of robbing adversaries of ammunition by mocking herself better than they ever could. In her home country, Lady Sovereign is a prime example of what’s known as a “chav,” a kind of beer-guzzling, Burberry-wearing equivalent of trailer trash. With her sideways ponytail and baggy Adidas hoodies, there is nothing classy or ladylike about her — a distinction she wears like a badge of honor. “I’m missing my shepherds pie / like a high maintenance chick missing her diamonds,” she raps.

For those who have followed her budding career via imports and the Internet, much of “Public Warning” will sound familiar. The production has been sharpened on songs like “Random,” “Blah Blah,”and “A Little Bit of Shhh,”but otherwise they haven’t changed.They’re all a couple of years old by now, but the album is more than just a repackaged best-of, partly because the new songs take her low-art to higher level.On the title track, a driving dance beat, skittering bass, crude guitar strokes, and retro video-game effects rush toward an ecstatic, fist-pumping conclusion that sounds like Atari Teenage Riot crossed with the Streets. It could be the song that makes her name in America.

A few numbers are clearly aimed at American listeners, while others are sure to elude them completely.”My England,” which opens with a mocking, flatulent horn march, serves to explode stereotypes about her home country: “Police carry guns not truncheons, make your own assumptions,” she raps. “London ain’t all crumpets and trumpets, it’s one big slum pit.”

The very next track, an especially clever and biting song called “Tango,” will be utterly inscrutable to American ears. The premise of the song is that women who wear liquid tans look like the Tango man, the bright orange character from a series of popular British soft-drink ads. There are additional references to a British cellphone network and the BBC comedy “The Vicar of Dibley.”

This is as it should be. After all, this is the same woman who ridicules her fellow Brit rappers for adopting American slang. “Some English MCs get it twisted, start saying cookies instead of biscuits,” she harangues on “Random.” The challenge will be to get Americans to start talking like her.