He graduated from the University of Dublin, was called to the Bar in 1776 and was elected a member of the Irish House of Commons for Donegal Borough in 1790.
He was appointed a judge of the Court of King"s Bench in 1792. On the murder of Lord Kilwarden in 1803, Downes succeeded him as Lord Chief Justice of the King"s Bench in Ireland. Downes was regarded as "the acknowledged father of the law".
According to Elrington Ball, after the murder 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 at great length, and was severely criticised by the Chief Secretary for Ireland, Sir Robert Peel, for so doing.