Drury was educated at Gonville College, Cambridge. Fighting in France, Drury was taken prisoner in 1544; then after his release, he helped Lord Russell, afterwards Earl of Bedford, to quell a rising in Devonshire in 1549, but he did not come to the front until the reign of Elizabeth I. In 1554 he sat as Member of Parliament for Chipping Wycombe. In 1559, he was sent to Edinburgh to report on the condition of Scottish politics, and five years later he became Marshal and deputy-governor of Berwick-upon-Tweed. He was a close observer of the affairs of Mary, Queen of Scots, and her house-arrest in Loch Leven Castle, and was in constant communication with Lord Burghley and wrote to him on 3 April 1568 regarding her escape from that place on 25 March about which he gave a full account. He went to Scotland with Sir Henry Gates and met Regent Moray in the Great Hall of Stirling Castle on 19 January 1570, and they had a discussion in his bedchamber after dinner. Moray was proceeding to keep an appointment with Drury in Linlithgow when he was mortally wounded, and it was probably intended that Drury should be murdered also. After this event, Drury led two raids into Scotland; at least thrice he went to that country on more peaceable errands, during which, however, his life was continually in danger from assassins. As ambassador with Thomas Randolph in April 1572 he stayed at Restalrig Deanery. There he plotted with Archibald Douglas to kidnap George, Lord Seton from the shore at Leith, but the plan did not take effect. In May 1573 he commanded the force which compelled Edinburgh Castle to surrender. A year later, a letter of the defeated and executed commander of castle, William Kirkcaldy of Grange came to light, which mentioned the jewels Mary, Queen of Scots had left behind in Scotland, and that Drury had taken some for a loan of £600. In 1576, he was sent to Ireland as President of Munster, where his rule was severe but effective, and in 1578 he became Lord Justice of Ireland, taking the chief control of affairs after the departure of Sir Henry Sidney. The Second Desmond Rebellion had just broken out when Sir William died in October 1579. Drury's letters to Cecil, and others, are invaluable for the story of the relations between England and Scotland at this time. His house in London gave its name to the street Drury Lane.
After Drury's death his widow married, in 1580, James Croft, the third son of Sir James Croft of Croft Castle, Herefordshire. Croft had served as a captain under Margaret's second husband, Sir William Drury, in 1578–9. The couple settled on property in Weston-on-the-Green, Oxfordshire, which had come to Margaret through her first marriage.
