He was born in either Lancashire or the Isle of Wight about 1560. He graduated from Brasenose College of Oxford University in 1578. Shortly thereafter he went abroad and converted to Roman Catholicism. 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. 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.
This led to their being summoned to London, where they were given the opportunity to take the Oath of Supremacy, acknowledging Elizabeth as the Supreme Governor of the Church of England. 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 Act 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 April 25, 1586.
He was beatified by Pope Pius XI in 1929.