THE US election video The Great Schlep contains just about everything you need to know about the woman some are calling the funniest comedian in the world right now. There's the sweet face which disarms you with its cuteness, and there's the perfect timing. "Hey, it's Sarah!" she says… (a pause, as bemusement quickly gives way to irritation) "Silverman?"

She's obviously intelligent, emphasising the importance of Florida in the race for the White House. She's passionate about her man – Barack Obama – and not afraid to reprimand fellow Jews who won't vote for him on race grounds. Blacks and Jews are just the same, she insists – they both like tracksuits and bling and "Yo!" is simply "Oy!" backwards.

It's the Democratic candidate's name that scares Jews; they think it sounds Muslim, she says. "Barack Hussein Obama – it's a super f****n' shitty name – but you'd think someone called Manischewitz Gooberman might understand that," she remarks. By this point, Silverman's comedy is staying the right side of permissible but is definitely getting scarier. Then she explains that Barack in Hebrew means 'lightning' and, as a cartoon bolt appears above her head, followed by a picture of Republican rival John McCain, she goes for it: "I'd much rather have a president whose name means lightning than one whose name means 'toilet' or a guy who f***s hookers." This is the did-she-just-say-that? moment, which is always quickly followed by the but-she-looks-so-innocent-with-that-ponytail! moment. Yes, she did just say that, and usually it's much worse.

This is Silverman on Aids: "If we can put a man on the moon, we can put a man with Aids on the moon, and pretty soon we'll be able to put everyone with Aids on the moon!" This is her on religion: "Everybody blames the Jews for killing Christ, and the Jews try to pass it off on the Romans. I'm one of the few people who believes it was the blacks." And this is her on 9/11, but only after grudgingly acknowledging that not everyone associates the date with learning that her favourite soy chai latte contained an alarming 900 calories: "If American Airlines were smart their slogan would be 'First thru the Towers'."

It's not known if Silverman, who is 37, will be flying American for her prestigious stand-up appearance in London on October 19. Although she performed at the 2006 Secret Policeman's Ball – "I listened to Madonna so's I could nail the English accent" – this will be her first headlining performance here and, with the DVD of her Jesus Is Magic show released the following day, is an attempt to break into Britain.

Will it work? Britain bans less, and is therefore harder to shock. The Jewish American Princess, whose self-obsession is only beaten by her self-delusion, is not one of our more recognisable figures of fun. This is a country which has only twice awarded its premier prize – the if.comedy award at the Edinburgh Festival Fringe, formerly the Perrier – to women and, when it comes right down to it, might prefer its comediennes to inhabit the Sunday evening slipper-time TV slot, preferably in a vicar's collar, rather than be this controversial. But there's no doubting the girl is a riot.

This is Silverman on getting older: "A couple of nights ago I was licking jelly off my boyfriend's penis and I suddenly thought: 'Ohmigod, I'm turning into my mother!'" This gag is quoted every time she's profiled by a man (including here). Yes, we men love jokes about the ageing process. We also love the pause halfway through, to let the first wave of laughter die down – we're so technical about comedy. Oh, and the pretty face-potty mouth combo is fairly irresistible, too.

If the YouTube clips from 1992 are typical, then Silverman started off sounding like so many other women in comedy: she slagged off men. But, with her frizzy hair and not-yet-perfect klutzy delivery, she seemed to be striving for bigger targets. Silverman was never going to be a feminist stand-up – too limiting. Now no-one is safe.

She's the third of four sisters from a liberal middle-class New Hampshire family, and with a drama-teacher mother and a father who taught her "bitch", "damn" and "shit" aged three, maybe she was always going to be a comedienne. It must have been traumatic to be a teenage bed-wetter – all the more when her hypnotherapy was abruptly ended by her doctor's suicide; Silverman learning of this just after it happened from her other shrink who was treating her for depression. But, looked at another way, this episode reads like yet another solid stand-up credential.

The last time she wet the bed was when she was sacked, by fax, from Saturday Night Live in 1994. She guested in US sitcoms and appeared in movies, usually as the male star's best friend's wacky girlfriend – all the time building up a formidable live reputation. Then in 2001 on a late-night chat-show she told how she ignored the friend who suggested she declare "I hate Chinks" to skip jury duty. She added: "I didn't want people to think I'm racist so on the form I wrote 'I love Chinks' – and who doesn't?" That was her big break in America; Britain probably knows her best for her "I'm F**king Matt Damon" video which generated 12.7 million views on Youtube, typical of her clodhopping candour.

Silverman doesn't like explaining her comedy but has said: "The person I am on stage is me. There's a kind of arrogance coupled with ignorance, and I see that reflected in our country." It is comedy for this politically correct age, when the rest of us spend so much time not saying what we mean and race is the elephant in the room. She's only joking, of course, and deep down would seem to have a heart. Last year at the MTV Awards, after Britney Spears' shambolic comeback attempt, she referred to the fallen pop idol's kids as "the most adorable mistakes you'll ever see ... as cute as the hairless vagina they came out of!" But she immediately regretted the quip, saying Spears "wasn't ready to laugh at herself".

Is Sarah Silverman ready for Britain? "People have been saying this is going to be my year for the past 12 years," she sighs. But this much is true: she's terrific on getting old. Have you heard the joke that goes... ?

• Sarah Silverman: Jesus Is Magic is released on DVD on October 13

• sarahsilvermanonline.com, and www.thegreatschlep.com