Regina Spektor, Hyde Park, London

If Florence Welch boasted a Voice so powerful at Glastonbury that it warranted its own capital letter, then Regina Spektor should make a call to her manager. Because while Florence has lungs so capacious she can distort the most hardy of sound systems, Regina has the range, the power, the vocal nuance and the intelligence to trounce her. In a "sing-off", Spektor would win hands-down.

And that virtuoso prowess was on display in abundance at this, the first of three concerts to be held in a tent next to Hyde Park's Serpentine Gallery. Those attending were treated to various warm-up acts as well as the main event, in a mini-festival-type setting that was fenced off from the riff-raff.

Eventually, several hundred of London's best-attired and sophisticated gig-goers crammed into a sweaty, dark venue to heroine-worship a 29-year-old, Soviet-born, highly-educated anti-folk New Yorker. As you do.

People love Spektor for her multifaceted eccentricities. At one point she is singing about a "poor little rich boy" reading Hemingway and F Scott Fitzgerald, the next she's whacking the furniture for the sound it makes.

Spektor is cosmopolitan incarnate. Born in Moscow to a violinist and music professor, her family emigrated to the US during perestroika. The burgeoning kook then studied under Sonia Vargas, a professor at the Manhattan School of Music, and spent a further four years honing her skills in another New York music college. She had time out at a butterfly farm as well as a spell in Tottenham (from the sublime to the bathetic). She then became part of the East Village's anti-folk movement, and her two most recent albums, 2006's Begin to Hope and this year's Far have both been critically well-received.

Tonight, Spektor bounced on like she was a 12-year-old performing at a barmitzvah, telling the crowd how amazing it was to be there before hunching over her piano. The acoustics in the tent weren't great; those who sidled in at the front to get a sidelong look were by far the most advantaged. At the back the lyrics were barely audible – and they are half the reason to listen to her.

But the crowd went wild as Spektor began with "Folding Chair" – "Just come and open up your folding chair next to me/My feet are buried in the sand and there's a breeze" – moving through an eclectic set with reggae, folk, pop and rock influences.

Other highlights were "Blue Lips", and "On the Radio"; as well "Laughing With God", the latter potentially a witty take on the capriciousness of an agnostic, or maybe Spektor was just saying that blasphemy isn't funny. People happily sang along to "Poor Little Rich Boy", the story of a middle class lad who moans when he has nothing really to moan about. "That Time" went down equally well, featuring the line "Hey I remember that time when I would only read Shakespeare", which presumably prompted much tittering of self-recognition at the back.

An extended encore included "Us", "Ghost" and "Fidelity", a treatise on not letting go in a relationship until you really love somebody, of which most people can dredge up memories ("I never love nobody fully, always one foot on the ground"). It's mind-blowingly obvious that Spektor has a college-load of talent. Listening to her songs in the privacy of one's home is enjoyable, but live, surrounded by her sometimes self-satisfied fans, is a different matter.

Tonight, these revellers screamed Spektor's name as though they were slowly drowning and were crying for someone to lend a hand. Others walked away saying: "This really isn't my cup of tea." At the end, I found myself somewhere halfway between the two.