It is full moon during the Hindu month of Phalgun and Maharaja Bakhat Singh is evidently having a whale of a time. Surrounded by the scantily clad ladies of his court, he stands waist-deep in an octagonal pool at the centre of his magnificent palace complex. During the springtime festival of Holi, it is traditional for celebrants to hurl pigment at each other, so the bare-chested Maharajah points a distinctly phallic syringe at his favourite girl, squirting her with a bright jet of coloured water. As a sitar-playing band strikes up, other members of his harem begin a sinuous dance. Nearby, yet more female attendants are smoothing down the flower-embroidered coverlets of two silk-draped beds. It is clearly going to be a long night. Even the clouds in the evening sky, writhing in excited coils, seem caught up in the festive mood.

Maharajah Bakhat Singh Rejoices during Holi was painted by so-called “Artist 3” of Bakhat Singh’s court in about 1750. The picture is one of 54 works in a remarkable new exhibition, “Garden and Cosmos: The Royal Paintings of Jodhpur”, at the British Museum. The assembled pictures, a once-in-a-lifetime loan from the unique holdings of the Mehrangarth Museum Trust, embody a little-known but deeply absorbing school of north-western Indian painting.

By contrast with the more celebrated productions of Mughal painting, the pictures of Jodhpur tend to be large in format. Their subjects are in many cases familiar – the entertainments of the court, the lives and loves of the gods – but the handling is boldly different. There is a wildness and erotic abandon about many of these works that is alien to much of Mughal art, with its fineness of detail and fastidious sense of sophistication. Celebration of Holi in a Garden Pavilion, painted in the late 1720s by “the Nagaur master”, is another explosively colourful depiction of the Maharajah and his harem engaged in the annual Hindu rite of dye-splashing. But this time the picture itself has been spattered with blotches of watercolour, so that it almost resembles a painting left out in the rain. There is still a certain courtly formality about proceedings, in that the impassive Maharajah, shown in profile and once more encircled by his adoring harem, has been carefully placed at the centre of the scene. But that only serves to throw the artist’s sudden boldness of gesture – an unexpected Indian prefiguration of Action Painting – into sharper relief.

The exhibition begins with an exploration of the evidently sybaritic court life of Jodhpur under Bakhat Singh, a man for whom every day was a new opportunity for sensual self-indulgence. Fornication was his favourite activity, to judge by the insinuating details that his court artists habitually inserted into scenes of otherwise innocent court diversions. A flock of copulating geese hint at pleasures that lie ahead for the Maharajah as he sits, being fanned by his ladies, at an outdoor concert. Even more striking than the mating geese is the untarnished silver pool in which they so energetically procreate. The surface of the water was painted in the medium of liquid tin, another Jodhpurian innovation.

The second part of the exhibition, exploring the artistic legacy of Maharajah Vijai Singh (1752-93), is chiefly notable for a series of fantastically busy, large-scale narrative pictures. Krishna frolics with the Gopi Girls in lush green forests. The hero-god Rama honours his pact with the monkey tribe, as exultant elephants dance in the monsoon rains. These panoramic images, thronged with colourful event, were actually used as aids to storytelling by the court poets of Jodhpur. It may not be entirely absurd to see them as early antecedents of the Bollywood movie.

But the most extraordinary pictures in the show are to be found in its third and last section, which is devoted to the reign of Maharajah Bakhat Singh’s great-grandson, Maharajah Man Singh. Man Singh turned to a formidably complex form of mysticism following his apparently miraculous delivery from near-certain death at the hands of his power-usurping uncle. On taking power in 1803, he dedicated his kingdom to the immortal ascetic Jallandhanarth. The result was an art of hypnotising religious intensity, full of haunting pictorial inventions, utterly different from anything to be seen in the earlier art of the Jodhpur courts.

Earlier generations of Jodhpur artists remain largely anonymous. But the name of Man Singh’s most gifted painter, Bulaki, has been passed down to posterity. He was a painter of great ingenuity and striking originality. The universe before time began is figured, in the left-hand panel of one remarkable triptych, as a completely void expanse of shimmering gold. Another series of Bulaki’s works marries the same bold spirit of abstraction with depictions of human and animal forms. Its symbolism has so far defeated scholars in the little-ploughed field of the art of Jodhpur. These pictures appear to allude to some creation myth, but their precise meaning is unknown. Kneeling figures and mythical beasts are set afloat on vast oceans of colour. Waves of time are rendered in the form of repeating whorls and coils of gunmetal grey, flame orange, and pearl white. These strikingly spare images buzz and pulsate, rather like the Op Art canvases painted by Bridget Riley in the 1960s. They were perhaps meant to assist in inducing a trance-like state of meditation on life’s higher mysteries.

The art of Bulaki is both high point and full stop. The increasingly esoteric court culture of Jodhpur was soon to be threatened from within and without. The caste of priests whom Man Singh had set above the aristocracy became increasingly mercenary, and corrupt. A cabal of disaffected nobles led a rebellion against him. Time was finally called, on his visions of eternity, by the advent of British rule in India.