Edmund de la Pole was handed over to Henry in the early 1500s as part of an Anglo-Burgundy peace treaty, and promptly imprisoned in the Tower of London, later to be executed by Henry VIII.
The reason why Henry took these attempts so seriously at the time, and by historians, is due to the level of encouragement and actual support these pretenders got from foreign princes.
In hindsight these attempts seem laughable - that a joiner's son should be crowned King by the Irish Lords, and that a Flemish man should be accepted as the rightful heir to England at the Scottish court.
What do you suppose these Cornishmen would have done if they had reached Henry VII, and been able to make demands on him? Henry may have lost face, and been forced to retract the tax, had the rebels had succeeded, but it is unlikely it would have led to him losing his crown.
The Cornishmen felt that it was unfair that they should be taxed to fund a campaign in Scotland, and that by tradition the northern counties should bear the brunt of this taxation.
On the 17th June, the rebels faced the King's forces at Blackheath - only a few miles away from London, and dangerously close to the royal arsenal at Greenwich.