"My father is always anxious to see me engaged in the Portrait,” the painter John Constable once complained to a friend. “But you know landscape is my mistress - 'tis to her I look for fame.”

This was a fame that posterity eventually brought him, of course. But in his lifetime he struggled. He wanted to get married to Maria Bicknell, the quietly intelligent, grey-eyed granddaughter of a formidable local cleric. But, for all that his prosperous mill-owning father was able to offer him some financial independence, it was not sufficient for a man with a family to support. The love-struck young Constable confronted an age-old dilemma: how could he keep both a mistress and a wife?

Portraiture offered an answer. In order to get his hands on that “necessary article cash”, Constable would accept commissions whenever they came his way. And that is why the latest exhibition of his work is being staged, perhaps rather unexpectedly, in the National Portrait Gallery. Constable Portraits: the Painter and his Circle opens this week.

Times Archive, 1937: Aspects of Constable: Centenary Exhibition at the Tate

The exhibition does full justice to the artist who in European opinion is England's greatest

• Times Archive: Culture

To Constable, his portraits must often have presented themselves as irritating chores. They took him away from his beloved landscapes. “I imagine myself driving a nail,” he wrote. “I have driven it some way, and by persevering I may drive it home; by quitting it to attack others ... I do not advance.” His friend C.R. Leslie, whose memoir of the artist (first published in 1843) became the standard biography, certainly did not much rate them. But then he was a man on a single-minded mission: to establish Constable's reputation as a great landscapist.

But about five years ago Lucian Freud, selecting works for a landmark Constable show in Paris, included several portraits. “I have always thought that it was completely loopy for people to go on about English portrait painters and not to have Constable among them,” he said. Now, perhaps infused with Freud's fervour while sitting for him, the critic Martin Gayford (whose charming Constable in Love is published to complement this show) teams up with Anne Lyles, the curator of the Tate's Constable Collection, to put on an exhibition that, weeding out several of Constable's stolidly awkward, wonky-eyed attempts, presents some fifty of his finest, liveliest, most sensitive or intimate works. These, ranging from early images of family and acquaintances, through the most tender mementoes of his courtship and married life to late commissions, allow us a first proper chance to assess his talents. This is an important and pioneering show.

Don't expect the grandiosity of Reynolds, the glitter of Lawrence or the slickness of Hoppner. Imagine setting off on that infamous picnic with Jane Austen's Emma. You might meet the local squire or an occasional society belle; and Constable himself - “the finished model of manly beauty” as excitable female neighbours reported (and a self-portrait sketch indeed proves) - can stand in as a beau. But you are far more likely to find yourself conversing with the rather dull rector, a bluffly jovial landowner or a fidgeting Miss Bates. Together, Constable's canvases build up into a rare but delightfully vivid portrait of a solidly respectable middle class.

As a student, Constable spent long hours in the life-room. He certainly had a feeling for the human form, as the luscious sensuality of nude studies can make clear. And his landscapes leave us in no doubt that he was a virtuouso painter. So why shouldn't he have become a great portraitist? As he finds his métier - the three-quarter length and three-quarter profile, and he was best at women - his works become more than competent money-spinners. He brings to his portraits that same passion for truth that he brought to his Suffolk scenes. The trouble is, that was precisely the problem as far as contemporaries were concerned. If his landscapes seemed too humble, too raw or too ordinary to those more inclined to Claude's classical poetries or sublime Romantic heights, then imagine how clumsy the portraits of his florid-faced sitters must have looked to those used to flatteries of an aristocratic elite.

Yet how frankly authentic they now seem. Look at Mrs James Pulham, a tour de force. There she sits, trussed up in her extraordinary confection of clothing, faintly ridiculous and yet possessed of a dignity that the artist confers by a tender attention to a facial expression that speaks of the complexities of the character beyond. Or go and see Mrs Edwards. You can almost hear the rustle of lace as she settles down, composing her face carefully as she no doubt imagines would befit a portrait. Her arms and hands appear almost to have been squashed in as an afterthought (perhaps to show off the rings).

Constable often seems to have had compositional problems. He has had to untack the canvas edge to fit Sir Richard Digby Neave in, and something very strange has happened to Mary Fisher's bosom and to Master Crosby's crotch. But where the painting matters - on the face - we can watch Constable working with a care and sensitivity that speaks less of professional skill than profound human sympathy. This is the feeling that animates his finest works. The grandiloquence of formal male portraiture clearly doesn't suit his inclinations (curators have judiciously excluded his full-length Rear-Admiral Western who looks suspiciously like the fish footman in Tenniel's illustrations to Alice in Wonderland). “Never mind the dogmas ... but get at the heart as you can.” Constable took this quote from Sterne as a motto.

See how affectionately he paints his family - including his father in a recently reidentified portrait (there is much new thinking in this show which, when it comes to so celebrated a painter, only emphasises how overlooked his portraiture has been), who sits as unbudgeable and rubicund as his fore-square red-brick house. Constable presents unadorned reality. He does not need to touch up the truth. He loves it for what it is. Sense how he cherishes his sister Mary: he softy strokes her with his brush.

A small oil portrait of Maria Bicknell was always carried with him. It was praised at the time for its “extreme” likeness. But the modern spectator can find more than that. The touch of the brush becomes literally touching as talent and tenderness merge. “Painting for me is but another word for feeling,” Constable said. He uses his brush to distil his affections. His precision of observation leads to emotional depths.

The spectator senses that deep familiarity that forms the bedrock of love. This is the love that underpins his finest works. Constable was not a great portraitist because he did not want to be one. But, where his feelings for a sitter become bound up with his feelings for the landscapes, he produces portraits of an intensity, subtlety and depth that, like his landscapes, speak the language of the heart.

Constable Portraits: the Painter and his Circle, National Portrait Gallery (www.npg.org.uk 020-7306 0055) from Friday until June 14

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