WILLIAM WARHAM was born at Church Oakley, in north-west Hampshire, around 1450. He later commemorated his parents, who died after the Wars of the Roses ended, with a brass in the Parish Church of St Leonard. The tower of his Tudor house survives in a later building in the village.

By the time of his own death (22 August 1532), the octogenarian Archbishop of Canterbury was out of favour with King Henry VIII, although he had earlier supported the King’s claims to annul his first marriage. His death saved the otherwise conscientious prelate from the indignity of martyrdom as he stood up to his royal master: the text of his intended defence against a trumped-up charge of praemunire survives.

The vicissitudes of 1532 and the spread of ideas for Reform, which inexorably led both to the annulment and the break with Rome, as well as to the 1534 Act of Supremacy, as Henry VIII tightened his Stalinist grip on the direction of the Church in England, were much in mind as I travelled from the bluebell woods of Oakley up to London for the opening of “Michelangelo: The Last Decades” at the British Museum.

This show, primarily of drawings, but also including letters, books, and paintings, takes up the extraordinary story of Michelangelo’s inventiveness from around 1533. It might be subtitled “What Michelangelo Did Next”.

By concentrating on his spiritual life in a time of international religious turmoil, it properly grounds him in his world, without all the predictable “Nudge, nudge, wink, wink” of sloppy 21st-century criticism that wants to find a gay man in every sacristy and a lesbian under every canopied altarpiece. Rather, Michelangelo’s religious sensibility shaped his response to the Renaissance as a man of faith.

England and the Catholic Continent were well versed in the rhetoric of Reformation when Michelangelo (or “Michelagnolo”, as he signed himself and was known to his first biographer, Giorgio Vasari) returned definitively from Florence to Rome (1534).

© The Trustees of the British MuseumMichelangelo Buonarroti (1475-1564), Christ on the Cross between the Virgin and St John, black chalk and white lead on paper (c.1555-64)

Rome in 1534 had not recovered from its sacking by the imperial troops in 1527, but it was also no longer the Rome of Pope Clement VII. Alessandro Farnese had been elected as Pope Paul III, and he set about an internal reform of the Church, all too aware of his own failings: he had promoted the careers of his four sons. At his death in November 1549, Cardinal Reginald Pole came second to succeeding him. Pole was an English aristocrat and second cousin of Henry VIII.

Pole was also a friend of Michelangelo. On one occasion, he offered to lend the old artist a pair of his spectacles to assist his failing sight. He was a member of the group around Vittoria Colonna, a sort of theological reading group known as I spirituali, increasingly thought subversive.

He died in November 1558, England’s last Roman Catholic Archbishop of Canterbury. Michelangelo outlived his patron and friend, dying in February 1564. By then, lines between Catholic and Protestant disputants had hardened, and the Inquisition sought to impose unilateral submission to Rome’s authority with as much draconian rigour as Edward VI and Elizabeth I employed in enforcing the new Protestant order.

The organisers of this exhibition cannot take us to the Vatican, into the Pauline and the Sistine Chapels, or bring the famed statuary of the Pietà or the Crucified to Bloomsbury, but the startling array of works on display, including architectural designs, engages us in that quest over three decades. It demonstrates how Michelangelo’s spiritual journey embedded his individual response over and against the Church, while allowing him to remain a devout Catholic.

This is a difficult thesis to argue, and suggests that Michelangelo trod a narrow line, but I was more convinced than not. The Benedictine Benedetto da Mantova had argued in his 1543 tract Il beneficio di Cristo that an individual’s response contemplating the crucifixion could bring the benefits of salvation, a mystical understanding dangerously close to the Lutheran tenet of “justification by faith”.

A single copy of that first sextodecimo Venetian publication (St John’s College, Cambridge, O.51.) survived the relentless attention of the Inquisition and after 1549 when it was placed on the Index of Prohibited Books. But drawings of the crucifixion were much valued by the group around Pole and Vittoria Colonna for private devotion.

He also took risks with iconography, moving away from a later medieval pious recapitulation of well-established themes and images. The recently restored cartoon of “Epifania” (BM) was in his studio at his death. Here, it is placed for the first time in nearly 500 years next to the workaday painted version of it by his mediocre pupil Ascani Condivi. It is, to say the least, unusual. Within a month, it was recorded as “three large figures and two boys, known as the Epifania”. No camels, no kings, and no gifts. What is going on?

© The Trustees of the British MuseumMichelangelo Buonarroti (1475-1564), study for “The Last Judgement”, black chalk on paper (c.1534-36)

In the centre sits a frosty Virgin Mary, a tight-lipped Harriet Walter character, who ignores the young Jesus. He has unaccountably slipped down between her legs on to a cushion. With her left hand, she restrains the greybeard next to her (usually recognised as St Joseph), to whom the infant Baptist is pointing.

But the most conspicuous figure in the composition is the man in a tight body armour, to the Virgin’s left, who gestures somewhat forcibly towards who knows what. Behind them is an array of four onlookers and a central woman who catches our eye.

As Michelangelo aged, much of his earlier fluency was lost: long gone the sinuous forms of the falling bodies from The Last Judgement and The Fall of Phaeton, but his sense of composition remained to the end. The tension and musculature of the backs of “the man rising” (1534-36) from The Last Judgement or of the soldiers from The Crucifixion of St Peter (c.1546) give way to the sketchier but more profound observations of Christ Crucified from the mid-1550s.

“Michelangelo: The Last Decades” is at the British Museum, Great Russell Street, London WC1, until 28 July. Phone 020 7323 8000. www.britishmuseum.org