Astonish, disturb, seduce, convince

Most people who like art would recognise a painting by Lucian Freud, who died last summer at the age of 88. His mature style is unforgettable. Today his reputation rests upon his unflinching nudes, craggy flesh-monsters seemingly sculpted out of encrusted paint. Even the pigment he used for pasty bodies, known as Cremnitz white, is unusually stiff and indestructible, saturated as it is with heavy lead carbonate. Benefits Supervisor Sleeping (1995), which sold for more than £17m at auction in 2008, typifies the monumentality of his pictures. An overweight woman lies, oblivious to our presence, on a careworn sofa. Freud paints the great mounds and gorges of her flesh, creating a cacophony of lived-in, mottled carnality. Under his eye, Sue Tilley (aka "Big Sue"), who modelled for the artist, becomes a symbol of abundance, a Venus of Willendorf for today.

Not everybody is enamoured with his approach – and you can understand why. Scrutinised with dead-eyed detachment, Freud's nudes are far from idealised. There is nothing flattering about them: no nip-and-tuck here, no graceful elision of blemishes or wobbly bits there.

The British artist Frank Auerbach, whom Freud painted in the mid-1970s, once described his friend's work as "raw". I would go further: the skin in his pictures, by turns bluish and tinged with yellow, suggests decay. Flesh may be massed before our eyes but the prospect of its disintegration is encoded just beneath the skin. More often than not, Freud's art has a brutal, merciless aspect.

Yet, as an exhibition of more than 100 of his paintings, drawings and etchings at the National Portrait Gallery makes clear, Freud didn't always paint in this fashion. During the 1940s and 1950s, his work, fraught with psychological tension, was rendered in a filigree linear style that earned him a reputation, in the words of the English art critic Herbert Read, as the "Ingres of existentialism". It was in these early years that Freud made an exquisite series of portraits of his first wife, Kitty Garman, (1926-2011), daughter of the sculptor Jacob Epstein. If there were a painterly equivalent of the phrase "love poem", then Freud's pictures of Kitty would be its definition. I encountered one of them recently on the walls of the Museum of Modern Art in New York.

Count the eyelashes

Girl with Leaves (1948) is a smallish pastel study of the head and clothed shoulders of Kitty, a pale-skinned brunette with mesmerising, slightly startled eyes. Above her, a solitary branch budding with leaves coloured a fierce, tart green unfurls like a praying mantis. Kitty stares past the viewer anxiously, like quarry flushed out of foliage. Tips of her hair stand on end, as though brimming with static electricity, an effect echoed by the spiky, serrated edges of the leaves. An encounter is about to take place. Something hidden and intimate may be revealed. The mood is charged with erotic frisson. But tenderness softens the sexiness, too, as the picture has been fashioned with obsessive precision (we can practically count Kitty's eyelashes).

The expression "to stop in one's tracks" is a cliché but that is what happened as I strode past this picture. It is a modest masterpiece, to be sure – less ballsy and brash than many other pictures in the museum's collection – but it practically glows with psychological intensity. To understand why Freud made pictures such as this – and why he stopped – it is necessary to learn a little about his life.

He was born in Berlin in 1922. His father, Ernst, was an architect and the youngest son of Sigmund, the founder of psychoanalysis. (Significantly, given his love of animals, Lucian preferred to emphasise his grandfather's early work as a zoologist.) His mother, Lucie, whom he would draw and paint more than anybody else, was the daughter of a wealthy grain merchant. Lucian grew up in a well-to-do apartment near the Tiergarten. On the walls were reproductions of famous works of art, including prints of Dürer's celebrated watercolour studies of a hare and a clump of turf. Dürer's hyper-detailed exactitude had a big impact upon the young Lucian. During the 1940s he, too, made meticulous studies of solitary animals (a dead monkey, a heron, a chicken in a bucket, a lobster) that are tours de force of prolonged observation.

After Hitler became chancellor in 1933, Ernst moved his family to England. Lucian attended Dartington Hall, a progressive boarding school in Devon, where he spent most of his time in the stables, skiving off lessons. Eventually his parents made him switch schools to Bryanston in Dorset, where he was expelled for pulling down his trousers in public. A forceful sandstone sculpture of a three-legged horse – the only three-dimensional work he ever made – won him a place at art school in London. Shortly afterwards he studied under the painter Cedric Morris in Suffolk – where one of his unextinguished cigarettes probably sparked a fire that destroyed the school – before enlisting in the merchant navy. He proved hopelessly impractical and lasted only three months after contracting tonsillitis.

By 1943, he had moved to Paddington, then a bombed-out no-man's-land in the west of London, and begun The Painter's Room, an important early work with shades of surrealism, in which a giant red-striped zebra's head (based on a stuffed trophy owned by Freud) dominates a room containing a threadbare sofa, a scruffy indoor palm, a bolt of red cloth and a top hat. Within two years, he was painting Lorna Wishart, née Garman ("The first person I got keen on," he later said). Once that affair was over, Freud took up with Lorna's niece Kitty, whom he married in 1948.

Subdued rapture

The note of subdued rapture that enters Freud's pictures in the late 1940s is pronounced. To see what I mean, you have only to compare Woman with a Daffodil (1945) with Girl with Roses (1947-48). In the former, with her lank hair, blue-green ghoulish complexion, downcast eyes and dark clothing, Lorna looks more like a depressed witch muttering a spell than a lover whispering sweet nothings. In the latter, Kitty, newly pregnant and clutching a yellow-pink rose like a talisman, appears radiant, alert, inspired. Her skin is smooth and white (aside from the faint smudge of a birthmark that Freud lovingly reproduces on her right hand). Brightness caresses her outline, almost like a full-body halo. The background is gilded and lustrous, like an icon.

The style is similar to Girl with Leaves (which came afterwards): the patterned dots on the stripes of Kitty's jumper are picked out one by one; each swirling gold-green iris of her oversized eyes is accented by the crisp reflection of a sash window in miniature. In tone, there is a similar back-and-forth between love and anxiety, too. The wicker backing of the chair offers a tense structure that in places has frayed and snapped. Silvery-white marks delineating individual hairs fizz with nervous energy. Hovering in front of Kitty's womb, the stem of the rose has several prominent thorns. She seems electrified, rapt, yet somehow on edge – ready in a flash to scarper or attack. Freud transformed Kitty into a Madonna for postwar Britain – an uncertain period of austerity following the ravages of war.

In other melancholic but beautiful pictures, Freud presents Kitty wearing a white dress or a dark jacket. We see her ill in bed in Paris and clutching a kitten by the neck. In the latter painting, he is surely punning on her name: that kitten with extraterrestrial eyes is a stand-in for Kitty herself, clasped tight in the grip of the artist's ironclad technique – subjected to what he once described as an "involuntary magnification". "I'm inclined to think of humans as animals dressed up," Freud used to say.

The sequence culminates with Girl with a White Dog (1950-51), bought almost immediately by the Tate, in which she appears older, more self-possessed and yet lonely. "To me, the earlier paintings show my mother as a girl, [whereas] this is a painting of a woman," says their daughter Annie Freud in a wonderful new BBC documentary directed by Randall Wright. "There's a sense of sadness, even some anger. It's to do with real life, the maturation of her face. There's a much more complicated person being portrayed here."

Sharp and wired

Kitty still wears a wedding ring, but the marriage soon foundered, thanks to Freud's entanglement with the society beauty Lady Caroline Blackwood, whom he married in 1953. Having swapped one muse for another, Freud shifted his painting style as the 1950s wore on, too. He began standing up while he painted and swapped fine sable brushes for coarser hog's hair bristles, resulting in a rougher, impasto surface. (Woman Smiling, from 1958-59, a portrait of his lover Suzy Boyt, is often cited as the turning point.) The limpid, lyrical approach of his early work was left behind for good.

“My work is purely autobiographical," Freud said – and the nervous energy that makes his pictures of Kitty so compelling can be compared with descriptions of his personality. The art historian John Richardson, who befriended Freud in 1942, recalls watching the young realist painter across the bar of the Café Royal in London, "as thin and sharp-profiled as a cut-out, standing on one leg like a stork, his eyes lowered in intense wariness". A few years later, a journalist described Freud as "a nervous man, whose eyes dart around like fleas in a snuffbox".

Ultimately this is what made him great: that complex, highly strung personality was writ large in every canvas. But in the pictures of Kitty we find something else as well: a delicacy and tender fervour that proclaims a young man desperately in love. "What do I ask of a painting?" Freud once wrote. "I ask it to astonish, disturb, seduce, convince." His paintings of Kitty Garman do all four.

“Lucian Freud: Portraits" runs at the National Portrait Gallery, London WC2 until 27 May. "Lucian Freud: Painted Life" will be broadcast on BBC2 on 18 February

Alastair Sooke is a presenter for the BBC's “Culture Show"