VIOLENCE and destruction have an unnerving and attention-grabbing quality that becomes more obsessive when the act is premeditated. The current exhibition at Tate Britain on Millbank neatly plays with this theme over 500 years of British history across the range of the permanent collections of the Tate.

Nikolaus Pevsner's economic description of the chancel screen of Holy Trinity, Toryban (1470-90), is hardly enough to draw attention to a medieval work of art in the heart of Devon: "SCREEN. Right across nave and aisles. Painted figures of saints in the wainscoting; tracery of type A standard; only one strip of decoration in the cornice; coving not preserved." But the outrage felt by many this summer when it was found that two panels had been hacked out of the screen by thieves is a measure of our response to how we now see art under attack.

St Victor of Marseilles and St Margaret of Antioch had stood side by side for more than half a millennium. They were among 40 saints guarding the sacred mysteries played out behind them, and offering to intercede for those gathered before them. Now they were heartlessly stolen and the screen had been vandalised.

This timely show offers a gallop through four different ideologies in whose name or under whose banner iconoclasts have worked. Religion, Nationalism, Feminism, and Modernism all have their place here, and the material evidence on show runs from the Dissolution of the Monasteries through the Puritan movement to the Irish Question, the suffragettes, the 1966 Destruction in Art Symposium, and into the contemporary world of the Chapman brothers, Mark Wallinger, Michael Landy, and Douglas Gordon.

That may sound indigestible and unintelligible, but the exhibition just about works, although it needs close scrutiny and attention to small details to understand much of what is going on. I rather fear that any visitors will treat much of the exhibition cursorily.

Two marble fragments prove to date from 1220 and to be from the shrine to St Thomas Becket (murdered 1170) in Canterbury Cathedral, and shards of painted glass come from Rievaulx, Furness, and the ruined choirs of Yorkshire. An otherwise undistinguishable lump of melted lead is apparently from an equestrian statue of George III.

Two chunks of granite masonry in a vitrine turn out to be fragments of Nelson's Pillar in the heart of Dublin, destroyed by the IRA in 1966. The 13-foot-high figure, the work of a local Irish sculptor, Thomas Kirk (1781-1845), and the pillar were erected in Sackville (later O'Connell) Street in 1808. It had survived 1916 and 1923, but, when it came down, local children sold fragments at 3d. an ounce. Nelson's head is now in the City Council's library.

One head that is here is that of King William III, commissioned from Grinling Gibbons by Dublin merchants to mark the victory of that Protestant king over James II at the Battle of the Boyne (1690) in 1701 and placed on College Green. As a potent symbol for Orangemen, the statue was repeatedly defaced, and, after it was blown up in 1836, parts of the figure had to be replaced, by John Smyth. The statue was eventually taken down after it was bombed on Armistice Day in 1928, an explosion heard eight miles away. The surviving head is an unremarkable replacement work; and the Tate is not saying in whose collection it is currently, nor how it came to be there after it was taken down for safekeeping in November 1928.

Even larger works need too much background explanation to make this an easy or satisfying exhibition. The Portrait of a Man with a Pair of Dividers (National Gallery) was once given to Gentile Bellini. A woman, Freda Graham, set about it and four other "Bellinis" with a cane in May 1914. Her action led to the closure of the gallery for three months, and prompted Wyndham Lewis to write scathingly of her in the first edition of Blast (July 1914). Even other suffragettes were moved to call for an end to these acts of petty vandalism.

But by then the "Rokeby" Venus had been slashed, and in a much later recording we can hear Mary Richardson proud of destroying one of Velázquez's greatest paintings.

The Second Book of Homilies (1563) offered a tripartite sermon "against the peril of Idolatrie and superfluous decking of Churches", warning the new Protestants of a reluctant Elizabethan Settlement of the hazards of images and worship. It stopped short of encouraging the wholesale destruction of images, but gave retrospective permission for the stripping of altars that had, in some parts of the country, followed the English Reformation. The right use of the church was crucial not just for the worship of God but for the social ordering of the land.

Perhaps the more poignant image for a Christian visitor to the show may prove to be the life-size Good Friday figure of the Dead Christ found in 1954 in the rubble beneath the former chapel of the Mercers' Company in London.

Carved from a single piece of limestone, shortly before the Reformation, the figure has been deliberately damaged in the five wounds, with the hands and feet hacked off. The crown of thorns has gone, and even the text of the great Pauline hymn at Philippians 2.5ff. has been smashed, no doubt because it was inscribed in Latin.

Here also is a fragment of the Virgin and Child from the great reredos screen at Winchester Cathedral. The surviving polychromatic decoration of the Virgin's mantle, and on her body, indicates how glorious such a screen must once have appeared in the middle of the 15th century, before it was taken down to be dismembered, presumably on 21 September 1538 as part of the Visitation to suppress shrines, although it may have (as the Elizabethan orders provided for) inscribed on a triptych. The Decalogue is painted in gold on the central black panel.

Unusually, the two side panels do not contain the Lord's Prayer and the Apostle's Creed. Instead, a selection of biblical verses encouraging sabbath-day observance (left) and godly compliance with ordinances and statutes appear on a rich crimson ground. In all the heated arguments over the Protestant cause in the Reformation, it never ceases to amaze me that the repeated justification lies always in the Old Law, and that the voice of the Word incarnate is silenced.

An almost identical board, also from St Mary's, which is similar in size (and not nearly ten metres in width as the catalogue states) encloses Elizabeth I's coat of arms with further biblical verses on the back of the side doors sermonising against Idolatry. It cites, but does not quote, 1 Corinthians 10.7-10, a passage used by the author of the 1563 "Sermon against perill of Idolatrie" which would have been familiar to the craftsman who painted the verses on the board.

"And Saint Paul warneth us to flee from the worshipping of them, if we be wise, that is to say, if wee care for health, and feare destruction, if we regard the kingdome of GOD and life everlasting, and dread the wrath of GOD, and everlasting damnation."

MICHAEL LANDY (b. 1963) is perhaps best known for his work Break Down, in which the 38-year-old artist destroyed all his material possessions, in an ordered and forensic way, in the basement of a former department store: birth certificate, car, clothes - everything was meticulously recorded, catalogued, and then destroyed.

At the Tate, he is represented by a similar work of documentary homage, H.2.N.Y. If the saw saws the saw and if the saw which saws the saw which saws the saw there is metallic suicide Marcel Duchamp (2007), which sits neatly alongside the discussion of the 1966 Destruction seminar in which Yoko Ono cut up her dress before a live audience.

Landy has this year been the artist-in-residence at the National Gallery, and his sculpture show there has been a crowd-pleaser, although, by the time I saw it, several of the automata had broken down or were off limits. Although the buttons no longer pressed, and the crank failed to turn, the simple idea amuses; figures of saints from paintings in the nation's collection have been turned into three-dimensional sculptures that whirr and collapse or explode.

By such quirky means, Landy has, I hope, led many to go to the Sainsbury Wing to see for themselves the works that had inspired his outrageously clever installation. His drawings richly combine more than a handful of images for each work and it could produce a useful trail for church groups to hunt up the many references to them.

Doubting Thomas, from the great Easter painting of Cima da Conegliano that hangs at the end of the enfilade of the galleries as you approach from the heart of the National, is reduced to a mere hand that jabs at the spring-loaded torso of the Christ.

St Jerome's act of self-flagellation brings together works by Cima (the naked outstretched left leg), Cosimo Tura (the ejaculatory upward reach of a figure in climax), and Ercole de'Roberti as a reminder of abstinence and of the danger of impure thoughts.

Landy was drawn to St Francis more than once, producing two moving statues, one a puppet-like frail piece from a small devotional image by a follower after Botticelli (1490/1500), and the other a headless cutout from Sassetta's Stigmatisation (c.1437-44), which had once been part of the high-altarpiece for the Franciscan church in Borgo Sansepolcro (Umbria).

Less successful, to my mind, was his attempt at a composite saint, combining the attributes and dress of five very different saints. The greaves of St Michael with Satan underfoot (Crivelli), the gridiron of Memling's martyred deacon St Lawrence, the wheel of St Catherine, and the eyes of St Lucy with the cloven head of St Peter Martyr, had all fallen into silence on the day I visited. With his engaging iconoclasm, Landy reminds us that the saints are all around us. 

"Art Under Attack: Histories of British iconoclasm" is at Tate Britain, Millbank, London SW1, until 5 January 2014. Phone 020 7887 8888. www.tate.org.uk

"Michael Landy: Saints Alive" is at the National Gallery, Trafalgar Square, London, until 24 November. Phone 020 7747 2885.

www.nationalgallery.org.uk