One of the best books from a folklorist's point of view is the esteemed Jacqueline Simpson's British Dragons (1980). She writes that:

The cult of St George, which was certainly of great importance in the history of British dragons, grew ever more popular towards the end of the Middle Ages. Having first won acclaim as a soldiers' patron during the Crusades, George was enthusiastically adopted by orders of chivalry both in England and on the continent.

According to legend, St George was a Roman soldier who was martyred in 303 for refusing to recant his Christian faith. There may have been other men by the name of George who contributed to the legend, adding wind to the saintly sail, but pinning down any one of them - and verifying the existence of them or this slain Roman soldier - is not an easy task. Indeed, it may be impossible. That aside, the oral tradition that embraced St George became a powerful thing. St George was placed in the role of the hero of the popular and widespread folktale, ATU 300, The Dragon Slayer, and that association in itself (with an oft-told folk narrative) may have been central in promoting George to popular hero in many places.

In answer to the follow-up by /u/ImitationFire, this has been addressed many times before in /r/AskHistorians, but it is worth repeating what has been said before - and what is eloquently expressed by Simpson in her book. People in pre-modern times believed that dragons once existed. They tended to relegate them to distant times or distant places. Much like giants, who were entities of former times, people were not likely to describe encountering a dragon in the way that they might say that they had seen a ghost or a fairy (which people believed existed among them in real time). Much is made of a reference in the Anglo-Saxon Chronicle describing a sighting of dragons flying around, but that may have been third-hand rather than a first hand observation. That said, a powerful atmospheric phenomenon could have been witnessed by someone who interpreted the power of the incident as having been caused by a dragon. That wouldn't have been impossible. But in general, people regarded dragons as long dead or living in distant, exotic locations.

The idea that the patron saint of England would have killed a dragon in the third or fourth century would have been completely believable. Those sorts of things occurred 'back then'.

Follow up question: how widespread was the belief in the existence of dragons in the Middle Ages?