Born in St Thomas near Exeter, he was the son of Gilbert Budgell, D.D.
He afterwards entered the Inner Temple, and was called to the bar but under the influence of Addison chose an alternative career.
Budgell assisted Addison with his magazine, The Spectator, writing 37 numbers signed X.
Budgell, who was vain and vindictive, fell on evil days; he lost a fortune in the South Sea Bubble and was accused of forging the will of Dr Matthew Tindal at the expense of his nephew, Nicolas Tindal.
Disliked by many, Budgell was criticized by Alexander Pope in the Epistle to Dr Arbuthnot and in The Dunciad.