Blessed Robert Drury attempted to appease Queen Elizabeth and her government as one of the Appellants. Two of the 13 who signed the Protestation of Allegiance would be executed during the reign of James I of England: today's martyr and Blessed Roger Cadwallador (in 1610 on August 27). The Appellants opposed the Jesuit methods of leading the Catholic mission to England and attempted to compromise, pleading a divided but honest loyalty--secular loyalty to Elizabeth's authority as the Queen of England; religious loyalty to Papal authority as the successor to St. Peter. The Appellants also opposed the authority and methods of the Archpriest George Blackwell, whom they thought favored the Jesuit approach. The Jesuit approach, articulated by Father Robert Parsons, was uncompromising: total loyalty to the Roman Pontiff and absolute refusal to adopt public acceptance of the Church of England while remaining privately opposed. The Jesuits would not tolerate Church Papists who attended Anglican services to avoid the fines and imprisonments, for example. The Elizabethan regime took advantage of these disagreements to encourage division among Catholics in England.
Even if Elizabeth I had accepted their appeal for relief to her Catholic subjects, the succession of James VI of Scotland ended this attempt--because he would not compromise, either. He demanded that the Appellants accept his authority over both religious and secular matters with the Oath of Allegiance. Members of the Appellant party were divided over whether they could take James I's new oath. Drury and Cadwallador were arrested and refused to take the oath.
According to the Catholic Encyclopedia entry on Blessed (then Venerable) Robert Drury:

