Pablo Picasso had a lot on, from shattering the western pictorial tradition with cubism to making sculptures from string and gloves. Why did he also produce a lifetime’s worth of fine art prints? Right through this show we see how he took on this refined genre in order to defile it, rubbing art history in the muck while giving it perverse, indestructible new life. The desecration begins with his 1905 print Salomé. Herod watches dead-eyed as Salomé dances naked, but Picasso lets us see more than the Biblical King as Salomé raises her left leg high in the air like a dancer at the Moulin Rouge. Already Picasso is depicting the body, as he said he wanted to, “like a blind man who pictures an arse by the way it feels”. This desire drives Picasso’s prints right through to his 1968 series Raphael and La Fornarina, in which the Renaissance artist and his mistress have sex in multiple positions while the Pope watches. The 86-year-old Picasso might be publishing a manifesto of what his life as an artist has been about – the body, not the soul. In the Vollard Suite, the great series of etchings created between 1930 and 1937, carnality fuses with high art. You see a bearded artist more interested in the head he has carved of his model than he is in the naked woman herself. The “real” model has a classical profile, but her portrait is a mass of protuberances and ovoids based on sculptures Picasso was creating at the time. The Vollard Suite is about the mystery of art, how it refuses to merely mirror life. It is also filthy. In another scene the bearded artist relaxes with his best mate the Minotaur. The man-bull hybrid and the artist raise their glasses as they cavort with two nude women, or the same woman two ways up, whose billowing breasts and hips are those Picasso typically gives his lover Marie-Thérèse Walter. Which is Picasso – artist or Minotaur? He is both, he says with self-mockery, as artist and monster enjoy their bacchanal like gangsters at a brothel. It’s not so funny when the Minotaur is a rapist. Or when he nuzzles his huge, stinking head with its matted fur close to a sleeping woman’s face. This is not Carry On Greek Myths. The Minotaur is a monster who ends up sacrificed in the arena. Earlier artists such as Titian and Rubens illustrated Greek myths but Picasso appropriates them, chews them up and produces his own new fairytales of sex and death. In a cathartic final image, the Minotaur has been blinded for its sins and is led through the night by a girl: Picasso hopes for redemption. The Vollard Suite is Picasso’s confrontation with his inner beast, but this 1930s masterpiece also faces the violence and irrationality of the fascist abyss. Next comes his 1937 comic strip The Dream and Lie of Franco, in which the eloquence of the Vollard Suite becomes a howl. Franco, leader of the far-right forces in the Spanish civil war, is caricatured with bristling rage as an onion-like pustule who sprouts phalluses, a brutish, murderous Don Quixote. The results of his violence stop you in your tracks. A woman screams at the sky while black lines of tears flow down her face. A mother runs out of her house with her baby in her arms, the awful way its head hangs upside down with gaping mouth and empty eyes telling you the child is dead. This devastating image of bereavement is enlarged on an epic scale in Guernica, reproduced here to make the point. There’s another affinity between Picasso’s prints and his anti-war painting: they’re both black and white. Picasso is at one with the print medium because it cuts everything down to the bone – to black lines on white paper. Women are always on his mind. The self-pleasing sexual fantasist who imagines he is a minotaur or satyr is also the most compassionate of political artists. In his eyes women are always the first victims of war, and mothers are its bereaved witnesses. His own much loved mother, whose family name “Picasso” he took, was living in Barcelona in 1937 at the heart of the war. Often in Picasso exhibitions you thrill, but then feel disappointed by his later works. I was tense, waiting for the falling off. Here it never happens. After the second world war, his prints don’t slacken but take on a crude art brut power. His 347 Suite, created in 1968, consists, naturally, of 347 prints – the British Museum owns them all. We get a joyful dollop of rollicking nudity, ogling artists and a caricature of De Gaulle. Picasso sides with the student revolution in Paris: a man in his 80s yet a child of the 60s. Still complex after all these years. Picasso: Printmaker is at the British Museum, London, from 7 November to 30 March