Charles Darwent on art: George Bellows was knock-out – but he was always playing catch-up

The star of the Ashcan School was influenced by the Impressionists. Yet for all the surface charm, his work shows a fear of what lies beneath

When good Americans die, they go to Paris; when bad Americans die, they stay in America. Thus, at least, thought Oscar Wilde. So where is the late George Bellows, who was both the most American of painters and the most French?

Bellows was not just American but from the Midwest, born in Columbus, Ohio. You might have pinned his later foreign tastes on his teacher, the Gallic-sounding Robert Henri, were it not that Henri was raised in Nebraska and born Robert Cozad.

Henri's cousin was the Impressionist painter Mary Cassatt, from a family so devoutly Francophile that they were known in their home town of Pittsburgh as the "Qu'est-ce que c'est Cassatts". The hand of France lay heavy on American culture, and the Impressionist hand in particular.

Which, in part, explains Bellows. When he went to study under Henri at the New York School of Art in 1904, Manet and Lautrec had already been supplanted in the French taste by Gauguin and Van Gogh. No one had told Henri, though, who preached the Baudelairean ideals of the painting of modern life as though Post-Impressionism had never happened.

Thus the subtitle to the Royal Academy's Bellows exhibition, Modern American Life. The irony is that painting life wasn't modern in Paris any more by the time Bellows got around to painting it in New York. Or at least, not Manet's version of life.

For Manet, modernity had meant depicting his own milieu – you can see it downstairs, in Manet: Portraying Life. This involved such things as picnics, black silk hats, asparagus and ladies in big frocks. Bellows was a devoted follower of Manet, as a quick wander through his show suggests. Pictures such as Summer Night, Riverside Drive aren't just Manet-like in subject but in handling. If this was all Bellows had done, you might come away from the Sackler Galleries thinking that Wilde had been right – that American Edwardian painters were just wannabe French ones.

It was not all that Bellows did, though. If his name occurs to you at all – it is not well enough known in Britain – then it is probably as a painter of boxers. Works such as Stag at Sharkey's are in the RA show, and brilliant they are, too. At best, Bellows's bravura handling of paint has something of Manet's feel for immanent light. But this is paint put to a different use. His few history paintings apart, Manet was not a politically engaged artist. (While the Paris Commune raged, he painted a croquet party in Boulogne-sur-Mer.) Bellows was politically engaged, though confusingly so.

He and co-followers of Henri were quickly dubbed the Ashcan School, in reference to the grunginess of their subjects. Where Manet might paint well-bred girls taking the air in the Tuileries gardens, Bellows painted badly bred boys diving naked into the East River in Forty-Two Kids. The brushwork of Bellows's Nude Girl, Miss Leslie Hall might show the hours he had spent studying Manet's play of light on female flesh in Olympia. But Hall is powerless, unattractive, the pathos of her position as Bellows's naked model a mark of her place at the bottom of American society.

If you go between the two Academy shows, in other words, you may be brought up short. Bolshie French artist paints silk frocks; bloated American capitalist paints slums: something wrong there. And there is something wrong, since neither artist's politics are straightforward.

Bellows's drawings suggest he is not the simple lyricist of the common man that he appears. The rickety slum children in Tin Can Battle, San Juan Hill, New York are indistinguishable from the pack of strays in Dogs, Early Morning. The blood-splattered heavyweights in Bellows's boxing paintings may seem to be victims of the plutocrats who have paid to watch them fight, but the boxers in Street Fight are animalistic. Beneath the modernity of the crowds in New York (1911) is something feral, something to be feared: democracy, the rule of the masses.

This horror at what lies beneath is most brilliantly shown in Bellows's paintings of the digging of the foundations of Pennsylvania Station. Excavation at Night can't help but remind you of Ground Zero, but then maybe that pit also hinted at a darkness in America's substrata. Bellows died in 1925, of a ruptured appendix, aged 42. The last room of this show sees him setting off in all directions at once, some promising, some not. Where would they have led?

To 9 Jun (020-7300 8000)

Critic's Choice

The hugely popular Light Show has extended its run, and opening hours. Head to London's Hayward Gallery till 9pm Thur, Fri and Sat to bask in the illuminating work of 22 artists, including James Turrell and Olafur Eliasson (to 6 May). Get mythical at Manchester Art Gallery with Raqib Shaw's paintings and jewelled sculptures (to 26 May).