When most people hear the word ‘cardinal,’ they think of the bird, the baseball team, or the guys with the funky red hats who elect the Pope. But there’s another type of cardinal—Anglican cardinals.
So why does the Church of England still have cardinals some 500 years after Henry VIII broke away from the Roman Catholic Church? The answer can be found in the original meaning of the title. ‘Cardinal’ comes from the Latin word cardo, which literally means ‘hinge’ but it also has the figurative meaning of ‘important.’ The title of cardinal was originally bestowed on senior priests who were permanently attached to a specific church. Although it came to be associated with clergy in Rome, cardinals could be found in other cities as well. It wasn’t until 1567 that Pope Pius V restricted the title to those affiliated with Roman churches. But by that point, England was a Protestant country, so the change in Roman Catholic practice had no effect there.
There are three clerics in the modern Church of England who have the right to style themselves as cardinals, and all of them happen to be in London. Two of them are senior members of the College of Minor Canons of St. Paul’s Cathedral (they style themselves ‘Senior Cardinal’ and ‘Junior Cardinal’), and the third is the Cardinal Rector of the parish church of St. Magnus the Martyr. The cardinals of St. Paul’s have borne the title since at least 1378; I haven’t been able to discover when the incumbent of St. Magnus the Martyr was first styled ‘Cardinal Rector.’
It’s a bit surprising that these titles were able to survive the waves of anti-Catholicism that swept through the Church of England from time to time, but the relatively humble nature of these positions probably allowed them to escape the reformist zeal of exuberant Protestants. It’s curiosities like these that make the Church of England, and Britain in general, so fascinating.
UPDATE (05/25/21): following the abolition of the College of Minor Canons of St. Paul’s Cathedral in 2016, the Rector of St. Magnus the Martyr is now the only cleric in the Church of England to use the title of ‘cardinal.’
 The College of Minor Canons was instituted to oversee the conduct of the daily liturgy. It originally had twelve members, but in 1840 Parliament reduced their number to six. Nowadays, the College has shrunk to three, though it is still responsible for liturgical matters. The website of St. Pauls has a page that gives a nice overview of the College and its work today. The College of Minor Canons is distinct from the College of Canons (whose principal function is to elect the Bishop), the Chapter (which administers the cathedral on a day-to-day basis), and the Cathedral Council (which serves as the cathedral’s ‘legislature’ and monitors the work of the Chapter).
 A grant of Pope Urban VI from that year specifically refers to them as ‘cardinals.’ The grant in question can be found in David Wilkins, Concilia Magnae Britanniae et Hiberniae, vol. 3, (London: R. Gosling, 1737) 134-135.