He graduated from Oxford University in 1578.
His feast day is 25 April. He entered the college at Reims in 1580, and there met William Marsden. The two were ordained to the priesthood there.
Upon finishing their studies, Anderton and Marsden set sail for England.
They were caught in a storm while crossing the English Channel. They prayed that they would be allowed to die on land rather than at sea.
They were driven ashore by the storm onto the Isle of Wight, and quickly seized by the local authorities. In court, they pleaded that they had not violated the law by landing in England, as their landing was involuntary, being forced ashore by the storm.
Although they acknowledged Elizabeth as their lawful queen in all secular affairs, they would not swear the Oath.
As failure to take the oath was considered treason under the Second Acting of Supremacy, Anderton and Marsden were found guilty of treason. The sentence was then confirmed, and a proclamation was published, explaining their guilt. They were taken back to the Isle of Wight near the spot where they had landed and executed by hanging, drawing, and quartering on 25 April 1586.
He was beatified by Pope Pius XI in 1929.