“Baroque: Style in the Age of Magnificence” is one of the richest, most sense-stunning exhibitions ever mounted by the Victoria & Albert Museum. This unmissable cornucopia of paintings, furniture, jewelry, costume, architectural designs, theatrical memorabilia (and much more besides) might itself have been modelled on one of the classic, courtly manifestations of Baroque style – the cabinet of curiosities, tightly crammed with wonders. An intimately lit suite of exhibition galleries has itself been turned into a labyrinthine cabinet of curiosities, in which space is found for all kinds of intricately wrought objects.

Where to start? There is the tankard embellished with writhing figures wrought in ivory, each one modelled on a nude by Rubens, as well as   the aphrodisiacal beaker made from the horn of a rhinocerus, carved with a scene of indelicate copulation. There is the ostrich egg cup, the clocks like miniature cathedrals, and articles of French furniture so ornate that years of patient work must have gone into their creation.

In the reverential gloom of rooms devoted to sacred art, the realisation dawns that the organisers have also managed to borrow the entire liturgical apparatus commissioned by King John V of Portugal for the most splendid chapel of early eighteenth century christendom – that of St John the Baptist, in the Chapel of San Roque, in Lisbon. Marvel at the  monumental gilt-bronze candlesticks, each so ornately decorated it looks as though barnacled with the golden forms of slaves, saints, apostles and putti. Wonder at the solid silver priest’s cribsheet, festooned with madonnas and  magnificent as a miniature altarpiece. Gawp at the the gold-chased cruets and salvers, and at the monstrance in the shape of a golden sunburst inlaid with rubies. Created by the finest Italian craftsmen, paid for by Portuguese gold mined in Brazil, this stunning ensemble of objects amounts to an exhibition within the exhibition itself.

A nearby display includes some vivid terracotta bozzetti from the hand of Gianlorenzo Bernini, the greatest sculptor of the seventeenth century – including the actual clay model for one of his most breathtaking creations, the altarpiece of the blessed Ludovica Albertoni in the church of Santa Maria in Trastevere, in Rome. The figure’s face has split but otherwise the saint’s form is preserved exactly as she emerged from Bernini’s profoundly theatrical imagination – an actress in a sacred drama, clutching her breast as she swoons in the orgasm of her spiritual visions. Look closely enough, so the experts say, and you can still see Bernini’s thumbprint, preserved in the wet clay as he moulded the body of the ecstatic saint.

Hung far above this small but thrilling object is an equally rare design on loan from the basments of the Works Office of St Peter’s, in Rome. It is an oil-on-canvas modello for the now-destroyed oil-on-glass window designed by Bernini to pierce the wall above the great Cathedra Petri in the cathedral itself. The bird of the holy spirit, centred to a sunburst, looks down with a fierce expression that has more of the eagle than the dove about it. Rents in the canvas have been visibly mended. This amazing object has been displayed – in a stroke of inspiration – as if it were a backlit shard of glass.

The Baroque was the art of a newly resurgent, triumphalist Catholicism. It was also the art of autocratic power. The British disapproved of both, choosing to execute the most autocratic of English Kings, Charles I, at the Banqueting House in Whitehall – virtually underneath the greatest work of Baroque art ever commissioned in this country, Rubens’s Apotheosis of James I. The symbolism was not accidental. To reject the king was also to reject his art; and in the world of the Baroque court, as the V&A’s show so compellingly demonstrates, art was indeed omnipresent. At every edge and threshold, at every corner and on every surface, images insisted on the immutable hierarchies of divinely sanctioned power. A pair of tiny horse ornaments fashioned for Augustus the Strong of Dresden encapsulate the Baroque idea of kingship itself. Each of these objects, which might once have dangled from his stirrups, is a miniature allegory of the ruler himself as Apollo: a staring round face of gold, with jewel-encrusted flames for hair.

The king, like the sun, was at the centre of everything. During court masques and balls, his courtiers danced around him, shaping patterns intended to mirror the concentric circles of the cosmos. When he was at the opera – that quintessential expression of Baroque style, with its fluid merging of all the arts – his seat was placed at the exact optimum position for the vanishing point of the scenographer’s perspective. A whole section of the show is aptly devoted to the performing arts, to models and props and instruments: a set of stage designs, or a basson in the form of a sea dragon. Such things have a mute poignancy, last relics of unimaginably lavish court entertainments, fit for kings who really did believe that they were gods.

Augustus the Strong borrowed his Apollonian imagery from Louis XIV, the most grandly Baroque of rulers. The Sun King’s greatest artistic legacy was arguably the palace at Versailles, itself an operatic, declamatory blend of architecture and horticulture. It is with Versailles court culture that the exhibition closes. This last set of displays, wonderfully rich in objects de luxe, includes a ground plan of the entire Versailles complex, with its grand avenues and alleys, its fountains and statuary, its myriad external and internal spaces. At the dead centre of the complex design is a tiny rectangle which corresponds to the King’s own bedroom. He is the sun at the centre of his universe, the hub at the centre of the wheel of the world. Yet the very nature of the design, with its proliferation of outwardly radiating lines, suggests another metaphor – that of a spider waiting watchfully at the centre of a web of power. “Baroque” is endlessly fascinating and essentially chilling.