It has long been a contention of mine that the Renaissance wasn’t really the Renaissance, at least not in the ways we usually understand the term. The desperate overemphasising of its civilising aspects that has gone on — the quest for geometric perfection, the rediscovery of antique knowledge and so on — tells us more about our delusions of progress than it does about the real ambitions of the 15th century. It has blinded us to some powerful truths about the era: its religious passion; its love of illusion. The fact that there was more of the Middle Ages in the Renaissance than we habitually propose has been shovelled under the civilisational carpet.

For a decent illustration of this important corrective, visit Renaissance Faces at the National Gallery. Certainly, there is no other overwhelming reason to see the show. No. That is wrong. Let me rephrase. Renaissance Faces is packed with superb examples of portraiture from the period, and as there are great things here by Titian, Holbein, Van Eyck and even Arcimboldo, you must witness them, of course. A surprising number of the exhibits come from the National’s own holdings and have merely been moved around the building. But novelty is never a worthwhile aim for any display. The more telling problem is not with the ingredients, but with the recipe.

The show is filled with marvellous things, but that does not make it a marvellous show. Alas, the exhibition-making here is horribly confused. Skipping between epochs, nations and methods like a gorging flea, this thoroughly mixed-up event has forgotten the cardinal rule of show-building: if you want us to follow, give us a journey.

To return to my opening salvo: in the absence of a proper route through the cornucopia of faces, the only successful way to enjoy these proceedings is to forget the usual exhibition need to join up some dots and to investigate each visage from scratch as you come to it. Which at least puts you in a decent position to see Renaissance portraiture for what it was: a hotchpotch of styles, methods, treatments and techniques; a scramble of tastes, looks, textures and fashions; a ratatouille of approaches, ambitions, outlooks and endgames.

This waywardness sets in from the first room, where we range crazily from a delicate French profile of a lady painted with exquisite precision by an anonymous Burgundian in about 1400, to Dürer’s startling portrait of a fiercely staring Johann Kleberger, from 1526. A trick of fashion makes Kleberger look more like a 19th-century composer than a Renaissance courtier, with his muttonchop sideboards and his Schubertian crop. How recent he appears. Certainly, portraiture has travelled a long way from the beatific French profile, but who ever doubted that portraiture was different in 1400 from what it became in 1526? What other agenda is being set?

This vestibule leads nowhere.

It’s every face for itself, then. And the most unlikely likeness in the opening spurt is Mino da Fiesole’s marble bust of the corpulent Niccola Strozzi, from 1454. This pear-shaped man sports one of the thickest double chins ever to be immortalised in Renaissance marble. His lack of idealisation is thoroughly surprising — even his hair looks greasy. Compared with Bellini’ adjacent masterpiece, Doge Loredan, with its stern grandeur and portentous realism, the porky Strozzi is almost a comic character, a Falstaff fallen among Lears. That his podgy humanity should have been preserved so unflatteringly raises a bunch of fascinating questions that a better show might have tackled.

Another of the event’s irritating decisions is the cavalier lumping together of northern and southern Renaissance pictures, which creates a shapeless stream of 15th-century output that roundly ignores regional variations and endemic cultural aims. Anyone who cannot value the differences in technique, tone, ambition, mood and pictorial dynamics between, say, Hans Memling’s walnut-hard portrait of a man in a black cap and Botticelli’s dreamy youth in a red cap is in the wrong business. A hard realist has been placed next to a soft dreamer. This is chalk and cheese.

Nothing meaningful unites the calm kingliness presented by Titian in his great standing portrait of Philip II, painted in 1552, and the ugly woman with monkey features recorded by Quinten Massys in 1513. One is a grand full-length, the other a grotesque head-and-shoulders. One is a picture with comic and sarcastic ambitions, the other — perish the thought — is most certainly not.

The only thing these two paintings have in common is the baggy coincidence that both were painted in the same century. The Massys and the Titian don’t hang in the same room, so some might argue that it is wrong to compare them here, but by doing away with chronology, regional difference, pictorial type and presentational purpose, the show sets any viewer free to make any comparisons they fancy. A clear case of too much freedom, say I.

So, home in on the most interesting faces and leave it at that. I was charmed by a colourful bust of a laughing boy, moulded in terracotta in 1498 and said to represent, amazingly, the young Henry VIII. If this is Henry, then what encouraging cheekiness the artist, Guido Mazzoni, discovered in his podgy toddler’s face. For sheer unexpectedness, though, nothing matches the self-portrait drawing made by Pontormo in 1523, in which the artist shows himself bulging out of a pair of Renaissance Y-fronts as he poses undressed in the mirror. Shame this is not a self-portrait show, where the image would have had a place.

The final room is where the grandest portraits of Renaissance leaders have been gathered: Titian’s magnificent Paul III, Raphael’s haggard Julius II, Anthonis Mor’s bellicose Phillip II. The unexpected appearance among these political giants of the Spanish Hapsburg court buffoon, Pejeron, also painted by Mor, offers a sudden counterpoint. In a show that is pitifully short of dramatic moments, here, at least, is a good one.

Renaissance Faces is at the National Gallery, WC2, until January 18

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