Even the Queen of England, said Andy Warhol, can’t buy a better hot dog than the bum on the sidewalk. Another thing the Queen of England couldn’t buy was a flattering portrait by Lucian Freud. When he painted Elizabeth II at the start of this millennium, he treated her face with the same harsh objectivity as any other face, a closeup of wrinkles and sags, tight mouth and unhappy eyes, under coils of grey hair, with the absurd addition of a crown. Was Freud a republican? He certainly wasn’t a sentimental royalist. This royal head rests uneasy on a wall of equally unvarnished portraits of famous and unfamous faces in the National Gallery’s addictive centenary blockbuster Freud show. It is a key to his art, for it is so movingly unpretentious – in an almost adolescent way – in its declaration of the artist’s moral mission. A portrait, says this portrait, must be brutally true. Face to face with a monarch, an artist has only two options: be a courtier or a truth-teller. Freud takes the path he always does, warts and all. His genius is his innocent simplicity. Just look and be honest about what you see. It was the clearest, most humble of creeds, yet it meant ignoring a truckload of philosophical and artistic distractions, over a long working lifetime. He’s clearly already electrically aware of his vocation in the first self-portraits in this show, out of which he stares at the world with huge eyes from a razor-sharp face. He flatters himself, surely? Yet photographs confirm he really was that good-looking. In his 1954 painting Hotel Bedroom, he stands in shadow, hands in pockets, brooding under hedgehog hair, while his new wife (he was on his second) Caroline Blackwood lies in bed in the foreground, pale and brightly lit, her hair tangled on the pillow, her long, thin fingers pulling at her cheek in apparent distress. It was their honeymoon. It’s a moment of anxiety and mystery in a young marriage, as we look from her pallor to his shadowy ferocity to a window across the street through which we glimpse inside another room, a theatre of different stories. Freud might be staging a fiction here, except it’s so grey and real. Very early on, this show makes plain, Freud rejected anything fanciful, surreal or mythological: as a young man he knew Picasso but didn’t share his modernism. Or his pal Francis Bacon’s theatricality. Blackwood later became a Booker-shortlisted novelist. They come at you so full of life in this show, the intense characters of Freud’s world, from his first wife Kitty Garman gazing abstractedly as she holds a kitten by its throat to Sue Tilley, whose magnificent mottled flesh fills your brain as you contemplate her in one of the last grand canvases here, Sleeping by the Lion Carpet. Garman and Tilley are painted in totally different styles, decades apart. One of the delights of seeing his art at the National Gallery is that, afterwards, you can have fun spotting his influences in its collection. In the 1947-48 canvas Girl with Roses, Freud paints Kitty as she painfully squeezes the thorny stem of a pink flower. You’ll find her cousins in Hans Holbein’s equally clinical Renaissance portraits. Seeing Freud in this museum of European painting takes him out of a boringly British context. It frees his early work from parochial comparisons with prosaic homegrown artists of the 1940s and 50s and instead makes you see his affinity with Holbein, Albrecht Dürer and Lucas Cranach the Elder. Born in Berlin in 1922, grandson of Sigmund Freud, brought to Britain by his parents in the year Hitler became chancellor – it’s no wonder Freud painted in his youth like a German Renaissance portraitist. Five decades later, he was trying to paint like Titian. You can compare his nudes with Titian’s two masterpieces Diana and Actaeon and Diana and Callisto, in the main collection, which he campaigned to buy for the nation. Titian’s two opulent displays of flesh pose bodies in complex interrelated groups – and Freud does the same thing in his epic 1993 painting And the Bridegroom. Two people are lying naked on a bed in this colossal masterpiece. Nearest to us is Nicola Bateman, a tiny, skinny, pale figure. Is she really that small or is it just that she is dwarfed by her immense husband, queer performance artist Leigh Bowery? His tanned flesh spreads mountainously beside her. They’re resting together on a grey-covered bed in Freud’s studio, while he patiently inspects their anatomies. He observes Bateman’s dimpled hips and her little foot resting on Bowery’s giant thigh, while Bowery – a heroic exhibitionist even at rest – lets us see the purple snake of his penis. It’s well in proportion with the rest of him: a bratwurst, not a frankfurter. It would be tempting to call this painting a butcher’s freak show, a cold comparison of two strikingly different bodies – except for the deep tenderness that pervades it. That gentle detail of Bateman’s foot making sure Bowery’s still there as she slumbers, with her curled-up, childlike sense of being protected, confirms this is a painting of love. But it was the giant who was vulnerable. Bowery would soon die after contracting Aids. Here are two humans defying all categories. Freud’s determination to tell the truth is not callous or chilly. It is, you can see here, profoundly attentive to our variety and our unity. Freud’s changes of style don’t really matter. His painterly means are not as important as the intensity of his purpose – to set another before him, in William Blake’s words. Grasping someone’s very being is what he wants to do. Sometimes he seems more like a sculptor than a painter: his people are so solid. Near the Queen, his portrait of David Hockney is as meatily alive as if you were standing next to the real Hockney. This is an ethic of art. Indeed it is a morality of life. And it surely has something to do with the fact that Freud lived when he and his brothers might so easily – as he told his biographer William Feaver – have “ended up in gas ovens”. Freud paints life in the face of death. In his 1968 painting Buttercups, a jug stands in a sink, stuffed with flowers. I’ve always wondered why Freud’s portrayal of plants always seem so sad. Looking at this, it’s suddenly clear. He pays such meticulous attention to each little yellow buttercup: this isn’t a painting of flowers in general, not even buttercups. It’s about these single specific buttercups – and they’re dying. Freud paints people the same way. His portrait of Bacon’s lover George Dyer is touching: Bacon painted Dyer in grandiose, tragic triptychs but Freud shows him as simply a beaten-up bloke, someone real. And someone who took his own life. Freud doesn’t flatter but neither does he despise. He is an artist for now, his lust for human physicality all-embracing. The Elizabethan age is over. The Freudian age lives on.