Lord Elgin, you let us down. With all the masterpieces of world art that Britain’s rapacious collectors grabbed from hither and yon, couldn’t they have got their hands on a single statue by Michelangelo? No, the only original work in marble by the great sculptor, painter, architect and poet in a British collection is a circular relief owned by the Royal Academy. What we have instead are extensive holdings of his drawings in the British Museum and Royal Collection. Unfortunately, the BM’s hushed use of these works on paper to try to illuminate his later life shows what poor recompense they are. The problem is disappointingly obvious from the start. After being moved by a portrait of the elderly, bearded, introspective Michelangelo by his most talented pupil, Daniele da Volterra, you’re plunged into his designs for The Last Judgment, painted on the altar wall of the Sistine Chapel from 1536 to 41. Michelangelo was in his early 60s when he returned to the scene of his earlier triumph on its ceiling to create his cascading, tumbling vision of bodies rising to heaven and falling to hell against a deep blue. Here are his sketches of swarming muscular nudes, struggling and fighting – or embracing? – all desperate to join the ranks of blessed. Yet I couldn’t tear my eyes from a projection of the actual fresco, or stop wishing I was there with the real thing, in the Sistine Chapel. Michelangelo’s monumental art isn’t so much timeless as always happening in the moment. The drawings, not so much. They are, perhaps surprisingly, less intimate than his bigger works. Maybe it’s because Michelangelo lived on a large scale, seeing himself as a hero. He was most himself when carving a colossus or putting a dome on a city’s skyline. Yet that needn’t make an exhibition of his drawings dull. This show manages it by taking the drama out of his life. There’s no mention of the risk and conflict that surrounded The Last Judgment, an intensely personal masterpiece. Even when he was still painting it he was accused of turning the Pope’s Chapel into a “bath house” by filling it with nudes. There’s no hint here of the gossip that underlay this, that Michelangelo was sexually attracted to men. Nearby the exhibition displays the drawings that helped cement that reputation: ravishing, highly charged scenes from Greek myth he drew as love gifts for Tommaso de’ Cavalieri, a young man for whom he formed a passionate, public longing. That’s quite exciting, no? In the 21st century, Michelangelo’s eloquently expressed and philosophically defended love for another man should make him a pioneer. But that’s not how this show tells it. Instead, it describes them as “friends” and avoids any erotic interpretation of the drawings. Thus Tityus, a lushly shaded image of a mighty eagle settling on a naked youth, is interpreted as a “warning against lust”, when anyone can see it’s infused with desire. Above it is a wall text selectively and misleadingly quoting one of Michelangelo’s letters to Tommaso. He tells Tommaso he is no more likely to forget his name than he is likely to forget to eat food: then a “dot dot dot” covers a crucial cut. What the ellipsis misses out is Michelangelo telling Tommaso he means more to him than food because while it only sustains his body, his beloved nurtures “both body and soul”. Body and soul. You cannot have Michelangelo’s soul without his body. Take away the body from Michelangelo and you deaden him. It doesn’t even take on the Neoplatonist ideas that shape his drawings. According to these, the love of beauty can lead the soul upwards to heaven: they allowed Michelangelo to show men embracing and kissing in The Last Judgment itself, visible here in this show when you look hard enough at a print of it. The exhibition is all too glad to move on from physical desire to theology. It makes much of Michelangelo’s friendship with the poet Vittoria Colonna. This relationship in letters and verse genuinely was chaste, as is pedantically set out. We are clearly meant to see Michelangelo’s friendships with Cavalieri and Colonna as exact parallels, equally asexual. But his letters and poems to Tommaso confess carnal longing as well as spirituality. And they reflect his lifelong passion for the male body in art. Drawings in this show of David on top of Goliath are part of a recurring theme in his art of young men subduing older ones, infused with sexual tension. This show is having none of it. Instead, it can’t wait to get him on his deathbed. It insists Michelangelo’s true preoccupation as he aged was his spiritual welfare. Powerful drawings of Christ on the cross are adduced as proof. But was he as unworldly as the show makes out? He was certainly obsessed with fame, hugely competitive and some said money-grabbing. When Vasari called him the greatest artist of all time, he wasn’t satisfied but told his life to his pupil Condivi. Both their books are in the show but there’s no exploration of the tales they are crammed with or the unprecedented nature of Michelangelo’s artistic celebrity. So much fun is excluded. Instead we get far too much of Michelangelo’s awful “pupils”. Michelangelo often let them do paintings based on his designs, and the show includes many of these awful daubs, tediously displayed next to the Michelangelo drawings they are based on. The worst of all is Condivi’s painted version of Michelangelo’s full-sized preparatory drawing or “cartoon”, owned by the British Museum, called Epifania. Still awake? If you are by this point in the exhibition, you’ve got me beat. I am obsessed with this artist, but I found it hard work. The exclusive focus on Michelangelo’s spiritual life short circuits not just his sexuality but also his artistry. Who is it aimed at? The Catholic Church may, I suppose, be happy. Michelangelo: The Last Decades is at the British Museum from 2 May until 28 July.