Every society portraitist wants to leave behind a portrait of society, and the greatest immutably define our sense of an era: Holbein’s Tudor court and Velázquez’s Habsburg one, Sargent’s new-moneyed fin de siècle, Warhol’s celebrity-crazed 1960s or David Hockney’s flatly cool 1970s. Fashion, furnishings and the aura of fame all play their part in such portraits, which deliver some of art’s most delicious, immediate pleasures. But are these things enough to fix the image of an age? Live Forever, Europe’s first retrospective of Elizabeth Peyton at the Whitechapel Gallery, is a test case.

Peyton belongs to a generation of mid-career American painters – others include John Currin, Lisa Yuskavage, Karen Kilimnik – who, in the past decade and a half, have made human figuration newly fashionable by unravelling Warhol’s legacy of finesse versus kitsch and satire versus fandom, his mix of high and low cultural sources, and his myriad uses of photography. Installed in long rows at the Whitechapel in a cathedral-like gallery that draws attention to their approximation to icons, Peyton’s tiny portraits read initially like one extended love letter to the big names of early 1990s art ’n’ pop ’n’ royalty.

Painted in enamel-like shrill colour, and derived from newspaper images of Oasis, Pulp and Nirvana, “Blue Liam” and “Flower Liam”, “Jarvis and Liam Smoking” and “Jarvis on a Bed”, “Blue Kurt”, “Princess Kurt”, and the doomed rock star Cobain as cute kid balancing a kitten on his arm in “Kurt with cheeky num-num” all look beautiful, young, glamorous, remote and somehow only half-alive. It is the same with the too-sweet off-duty images of Princes Harry and William, the washed-out fleeting hero in “Celebrity (Leonardo DiCaprio)”, the droopy poses of the artists in “Piotr” [Uklanski] and “Maurizio [Cattelan] Eating”.

Peyton’s medium – mostly thin oil paint applied to board, which has none of the absorption of canvas – emphasises the hard artificiality of what appear to be soft, ragdoll bodies. Equally paradoxical is her small scale, implying intimacy but delivering distance: no one meets your eye; languor, indifference, passivity replace psychological insight. Friends and lovers – sometimes painted from life, though you wouldn’t know it – have identikit bland faces and offhand stances. Many are depicted asleep, supine, or, like the messy “Julian with a Broken Leg”, on crutches. “Savoy (Tony)” lies in a froth of white linen and violet covers, his joined arms as feathery as a curl of silk in Boucher or Fragonard. “Spencer Drawing” is a horizontal pink figure, too listless to lift his candy-hued crayons. In “Haircut (Ben and Spencer)”, the pampered victim flops into a limp diagonal, offset by the arabesques of his elegant chair and sweeping balcony.

The sense of a privileged class slumbering its way into oblivion is Peyton’s unique contribution to 21st-century portraiture, though her methods are in no way formally inventive. Stylisation, economy of line, sharp angles and tightly cropped close-ups reminiscent of snapshots are all derived from either David Hockney or Alex Katz – and make you long for the vigour and rigour of either – while the androgynous neutrality of most of her cast is a Warhol legacy. Among historical figures, it is interesting how often Peyton chooses those associated with homosexuality, and imbues them with pathos: “Flowers and Diaghilev”, “Ludwig II of Bavaria”, depicted in a variety of extravagant gestures, caressing a bust of Marie Antoinette, parading in Versailles. A purple-hued “Silver Bosie” wishes Oscar Wilde’s nemesis into a kinder, gentler figure than history records.

Like Stella Vine, a similarly arrested adolescent painter, Peyton is an illustrator and a fabulist, conjuring a fin-de-siècle fairytale from the way we live now. The ink drawing “Kings and Queens” depicts a 19th-century woman surveying a royal canvas in gilt frame: an intent look at looking. In self-portraits, Peyton depicts herself reading, absorbed in a fictive world that protects her from the need to engage with us.

Except that her half-fictions do tell half-truths – about our craving-yet-distrust for painterly beauty, about the allure of portraiture long after the formal society on which it was built has disintegrated. The single best painting in this show is the chill, chiselled, vampirish “Zoe’s Kurt” – a vanishing act in which skin and hair fade to a whiter shade of pale, the body is dashed with weeping trickles of paint, the jacket is a dance of abstracted red marks and only crimson magazine-fantasy lips remain in focus. Does Peyton critique or merely comply with the virtual realities of our image-overload, celebrity-drenched times? Perhaps it doesn’t matter: though she is maddeningly self-absorbed, sickeningly ingratiating, her decadence is our decadence, and in her convalescent subjects lie her theme and her battle – the disappearing of a tradition.

‘Live Forever: Elizabeth Peyton’, Whitechapel Gallery, London E1, to September 20, tel: +44 (0)20 7522 7888. Sponsored by Banana Republic

Jackie Wullschlager reviews the book ‘A Face to the World: On Self-Portraits‘