(Royal Academy, London, until 25 January 2015)

He’s a familiar sight in the National Gallery. A young tailor has been distracted in the middle of his work. Resting his scissors on the table for a moment he glances up, as if you’ve just wandered into his workroom, half-inquisitive, half-challenging. His clothes are simple but well-made, showing off his craft: his cream doublet is elaborately pinked and finely-detailed lace peeks out at collar and cuffs. In a moment his assessing gaze will shade into something more specific: a frown at being disturbed, perhaps, or a welcoming smile, but for now he’s captured in that split second where everything is still possible: a moment of infinite potential.

Giovanni Battista Moroni, a 16th-century painter from Bergamo, was a master at conveying that unsettling quality of naturalism. Artists throughout the Renaissance had been praised for the ‘speaking likeness’, the kind of portrait where the sitter seems on the cusp of talking to you, but Moroni’s portraits go beyond that. His sitters not only seem to be aware of your presence: they seem to watch and weigh you, judging your quality. To look at one of his pictures feels like stepping into a dialogue with the past.

Moroni was born in the early 1520s, more or less at the time that Raphael died and only a few years after Leonardo’s death in France; Michelangelo was forty-five when he was born. It’s strange to think that he was so early: his portraits, in particular, have little of the Renaissance about them. If Moroni’s works echo any of the great masters, it’s Titian, who was some thirty years older than him; but we’re not sure if they ever actually met. In a way, Moroni invites comparisons with later painters born shortly before his own death: his psychological intensity would be echoed in Rubens’s portraits, and the pared-down, freeze-frame quality of his compositions would be developed more famously by a painter who was only eight or nine when Moroni died and who’d been born a mere sixteen miles away from Bergamo in the little town of Caravaggio. Moroni himself trained with Moretto da Brescia, a successful artist whose works are still very much of the Renaissance, but who also painted penetrating portraits like that of Fortunato Martinengo Cesaresco (National Gallery), which must have had quite an impact on his young pupil.

The exhibition doesn’t include every picture by Moroni because that would be impracticable and, besides, it’s in the Sackler Galleries so there isn’t enough space; but what it does do, rather well I thought, is to give us a rounded picture of Moroni’s artistic output. The portraits are his most memorable and successful works, but the show makes the point that he also received commissions for religious pictures. These are where we see much more of Moroni’s Renaissance heritage coming through and we see explicit examples of the young artist reacting to the past: his Trinity, for example, painted in his early thirties, which is a direct reworking of a composition by Lorenzo Lotto executed thirty years earlier (conveniently hanging alongside it here). Of the two, I found Lotto’s original more attractive. It has greater softness and mysticism, whereas there’s something hard-edged and less fluid about Moroni’s: something a bit too didactic and a bit less suggestive. But that’s telling: Moroni had spent some time in Trent at exactly the time the Council was laying down new rules about the role of art in promoting Catholic doctrines and religious narratives.

He is more accomplished in his striking portraits where we see his sitters in contemplation of the Madonna and Child or the Baptism of Christ. These aren’t like the Renaissance sacra conversazioni where patrons implausibly turn up kneeling, eavesdropping on the Madonna and saints. On the contrary, the sitters are engaged in the kind of religious meditation encouraged in the Counter-Reformation world, and it’s as if we are somehow miraculously seeing with their inward eye and sharing their visions.

But the most spectacular aspect of Moroni’s work will always be his portraiture. The room of aristocratic portraits in the exhibition is simply ravishing: every picture is a masterpiece and every sitter has an air of enigma sufficient to inspire a novel. And the fabric painting…! Indeed, if you’re liable to get bored by me rhapsodising about Renaissance costume, I’d just cut your losses now and skip to the last paragraph, because here there are enough soft velvets and cool satins, gold braids, dagged and frayed edges, pleated cuffs and blackwork collars to keep me going for hours. My personal highlight in this room was the Portrait of Giovanni Gerolamo Grumelli, commonly known as The Man in Pink for obvious reasons. He wears a splendid rose-coloured suit with doublet and hose embroidered with floral motifs in silver thread; seed pearls and braid decorate his knee garters and his shoes are of slashed rose velvet; even the blackwork on his collar and cuffs is pink. It’s important to remember that at this date pink was considered to be quite a manly, virile colour: it was a shade of crimson, the high-status colour of senatorial robes, and thus a perfectly appropriate colour for well-born young men.

And indeed, Grumelli looks like the kind of man it would be unwise to cross. He glances out at you, wary and considering, perhaps with a hint of mischief in the slight tilt of his eyebrow. He stands in a blaze of Renaissance grandeur among the fragments of antiquity, with a new dawn just showing above the crumbling, ivy-covered wall. He’s twenty-four years old and the world is at his feet. And one of the gifts the world offered him, a year after this portrait was painted, was Isotta Brembati, whom he married after the death of his first wife. She hangs beside him in the exhibition: a shrewd and redoubtable lady. Indeed, she seems more than a match for her pretty young husband. She wears a marten fur as protection against death in childbirth (is that how Grumelli’s first wife died?), but the most striking thing about the portrait is her gown, in stunning green and gold brocade, set off with an unexpectedly frivolous fan of pink and white ostrich-feathers. And her jewels are gorgeous too: the light dances on the curve of her pearls and plays in the depths of the garnet beads around her neck. She looks every inch the prosperous matron: it seems that neither she nor her husband felt the need to advertise her talents as a poetess.

If you crossed Isotta, you might pay for it with a sonnet or two, but some of Moroni’s sitters could deal with you in a decidedly more conclusive kind of way. His portrait of Gabriel de la Cueva is a wonderful example of coiled power: this Spanish grandee served as Governor of Milan for seven years from 1564 and Moroni painted him four years before his appointment. The man we see here is an ambitious, worldly courtier waiting for his moment: he has a Spanish taste for luxurious understatement and his doublet is embroidered black-on-black, that most expensive of colours, while the crimson embroidered velvet of his hose is slashed to show silk beneath. He appears calm, even at ease. Unlike young Grumelli he doesn’t pose: he leans back, feigning nonchalance, against a plinth. But the sword at his side is no aristo plaything but a serious piece of kit, and he stares out at us with calculating, narrowed eyes; if we needed any further reason to be wary, his motto on the plinth would give it to us: ‘Aqui esto sin temor y de la muerte no he pavor‘ [I am here without fear and I have no dread of death]. Attaboy!

He’s matched for swagger by Faustino Avogadro, who hangs here beside his wife Lucia Albani Avogadro (both usually found in the National Gallery as well). Faustino is determined to show us his martial glory: he wears a buff jerkin over chain mail and his very serious-looking sword denotes him a warrior, even before you notice the decidedly over-the-top tournament helm propped on the side with its profusion of plumes. Usually you’d be tempted to dismiss such a man as a swaggerer, the kind who tells endless stories of deeds that probably never happened. But Faustino was a dangerous sort. By marrying Lucia he’d got caught up in her family’s feud against the Brembati (Isotta’s family), which culminated in 1563 when one of the Brembati nobles was murdered in church. Faustino’s servant was arrested as one of the murderers, which made it clear enough where the guilt actually lay; Faustino and Lucia fled Bergamo and went into exile. For all his posturing, Faustino’s end was rather undistinguished: he apparently fell into a well while drunk (although, having read too many novels, I can’t help wondering whether he fell or was pushed).

All these faces are full of stories and if I said all that I wanted to say about each one, we’d be here forever, so I’m going to limit myself to just a few more. In the following room are a few more intimate portraits, always with the same degree of psychological acuity, among which is the gorgeous Portrait of a girl of the Redetti family. This child, who can’t be more than three years old, is dressed in a miniature version of adult’s clothing: black-on-gold brocade, with a pleated ruff and cuffs and a string of pearls around her neck. More pearls are twined in her hair and she wears a little earring with three seed pearls set in it; you can just glimpse the coral bracelet she wears as protection against the evil eye. But what’s most remarkable about this little girl is her air of self-possession. She is dressed like an adult; she has the cautious gaze of an adult; and yet Moroni doesn’t make her look remotely adult-like, in contrast to so many painters at this period who had immense trouble painting children. She must be one of the most delightful painted children of the century.

The final room displays some of Moroni’s later portraits, including my beloved Tailor. These lack some of the glamour of the showy aristos in the earlier room, but Moroni continues to probe into his sitters’ souls. His portrait of Antonio Navagero is delightful, though probably not for the reason the patron intended: Navagero’s sober fur-trimmed gown reveals a suit of surprisingly tight crimson satin, with a short doublet, narrow breeches and the most insistent codpiece in the entire show: an ensemble which sits rather ill at ease with his cheerfully ruddy, round-cheeked face and the threads of silver in his beard. Despite the surviving descriptions of Navagero as an ‘intelligent’ and ‘prudent’ man, who served with ‘care and diligence’ as podestà in Venice, you can’t help thinking that he’d be the kind of dinner guest who’d drink more than his due, tell riotous stories and end up trying to chase the maidservants. Poor Navagero.

A more distinguished picture is presented by Giovanni Gerolamo Albani, which shows Faustino Avogadro’s father-in-law and fellow conspirator against the Brembati family. This magnificent old gentleman wears a sumptuous amount of ermine and his clothes are all black – which, remember, was the most expensive dye – while a jewelled crucifix hangs round his neck. Unlike every other sitter in the show he meets our gaze squarely and without wariness. He has been distracted from reading his book; he seems about to rise from his chair; but for now he just studies us with the politely indifferent air of a patriarch who fears nothing.

Giovanni must have already known that Moroni would do justice to him, because the portrait was commissioned under flattering circumstances. Giovanni had (so they say) been in Venice, where he’d visited Titian and tried to commission a portrait. On hearing that he came from Bergamo, Titian had asked in some surprise why Giovanni wished to commission a picture from him; he advised him to get one from the talented Moroni instead. It’s a good story and probably did Moroni no end of good when it circulated in Bergamo. Personally I don’t believe it for a minute, because Titian was a canny fellow and I can’t imagine him casually turning away trade; but it makes a good tale.

And Moroni deserved such praise. Every time I go to the National Gallery I stop for a moment in front of his portraits – they’re on my personal highlights tour – and I really hope this exhibition will introduce him to a new audience. With his realism, his dazzling technique and his perceptiveness, Moroni is one of those painters who feels startlingly modern and whose pictures erase the five centuries that separate us from him. He deserves to be better known and I urge you, if you’re in London, to visit the RA and to encounter him for yourselves – and to make the acquaintance of this gallery of lords, ladies, clerics and rogues who populate his stunning portraits.