Downes was the second son of Robert Downes of Donnybrook Castle, Dublin, MP for Kildare, and his wife Elizabeth Twigge, daughter of William Twigge, also of Donnybrook; he was a grandson of Dive Downes, Bishop of Cork and Ross and his fourth wife Catherine Fitzgerald. The Downes family came originally from Thornby, Northamptonshire. He was related to the influential Burgh and Foster families and, through his FitzGerald grandmother, to the Earl of Kildare. He had an elder brother Dive, who took holy orders; Dive died in 1798. Their father died when William was only three.
Downes was regarded as "the acknowledged father of the law". The low opinion held of him by his predecessor as Lord Chief Justice, John Scott, 1st Earl of Clonmell, who called him "cunning and vain", can be disregarded, as Clonmell disliked and despised most of his judicial colleagues and was never fair to them. In general Downes was respected for his integrity, although his manner was stern and intimidating, and it was said that he never laughed. According to Elrington Ball, after the death of Kilwarden it was generally agreed that only Downes was fit to succeed him. He was one of the few judges whom Daniel O'Connell could not intimidate. At the trial of John Magee for seditious libel in 1813, O'Connell's conduct of the defence was so intemperate that another barrister said that he should have been prevented from speaking; Downes said drily that he personally regretted not having prevented O'Connell from practicing law in the first place. On the other hand, Downes did let O'Connell speak in defence of his client at great length, and was severely criticised by the Chief Secretary for Ireland, Sir Robert Peel, for so doing. He took a severe view of any form of judicial misconduct. In 1803 the author of a series of scurrilous letters attacking the Government under the pen name Juverna was exposed as Robert Johnson, a justice of the Court of Common Pleas. Downes drove hard for his prosecution and conviction on the charge of seditious libel and his enforced retirement from the Bench. When Johnson tried to evade prosecution Downes had him arrested, telling him sternly that his attempt to evade justice was as great a crime as the libel itself. He retired in 1822; despite his considerable age, and the fact that he had neither wife nor children, he accepted a peerage, and was created Baron Downes, of Aghanville in the King's County, with a special remainder to his cousin Ulysses Burgh. Ulysses was the grandson of William's aunt Anne Downes, who had married Thomas Burgh. He succeeded William as second and last Baron Downes. William lived at Booterstown, County Dublin.
Death and burial
When he died he was buried in St Anne's Church, Dublin next to his judicial colleague William Tankerville Chamberlain, who had been his inseparable friend for many years: "their friendship and union was complete...and now by the desire of the survivor they lie together in the same tomb" according to the epitaph.