From this website:
The Inn dates back until at least 1364, when it was owned by the Teynturer family. The naming of the Inn may have been connected with the Guild of Saint George — William Teynturer (the younger) left property in his will to the Guild in 1376.
Between 1590 and 1624 a Free School was run in one of the Inn’s rooms. Subsequent to that, it was ordered that plays should only be performed in the Old George Inn ‘the size and form of the inner courtyard being well adapted for that purpose’