I understand this may depend on various factors, but I am interested to find out whether many/some/any people in 13th century England would have knowledge of the stories out of Greek mythology. Specifically, an east coast port town, if that would make a difference.
If so, would this knowledge have been limited to any social class more than others, or depend on a certain level of education/literacy?
Third, what was the most likely source of this knowledge?
Quite a bit, actually. Graeco-Roman mythology was a significant part of the education curriculum. Much of the educated elite would have been broadly familiar with ancient Greek mythologies through its Latin form, albeit overlaid with a Christian point of view.
In High Medieval England, an anthology of six works known collectively as the Liber Catonianus (aka Sex Auctores) became a standard textbook of sorts. Widely used in English schools, they notably included:
Together, these texts provided medieval English students with a somewhat surprisingly rich education in ancient Graeco-Roman religion and culture.
Both Claudian and Statius were Ancient Roman poets, while the Eclogue is dated to between the 9th and 10th centuries, written perhaps by a Saxon theologian called Gottschalk of Orbais. A translation is available here, which gives you an idea of what a 13th century student in England would've known. It contains many Graeco-Roman myths familiar even to a modern audience, for example the myth of Proserpina. Moreover, its status as a standard text for instruction means we can expect the educated class to be reasonably familiar with its contents.
Much of the myths related by the Eclogue would also have been widely available in the form of two more sources: Metamorphoses by Ovid, and the works of Virgil. Both Roman poets drew considerably on Graeco-Roman mythological traditions, and were held in extremely high literary esteem by Medieval Europeans. Virgil's Fourth Eclogue was even perceived as a messianic prediction of the birth birth of Jesus. Their popularity during the Middle Ages was a significant influence on writers of the time: Metamorphoses clearly had a big impact on the works of Chaucer, for instance. Given their status as Medieval pop culture blockbusters, most educated people in the 1200s were likely familiar with their works.
Note that all of this were Latin, at the time the lingua franca of Western Europe including England. The relative abundance of information on Classical mythology were likewise transmitted from mainly Romans via Latin poetry. Whatever knowledge of Greek traditions existed was, therefore, filtered through a Roman viewpoint.
Further Reading:
Orme, Nicholas. Medieval Schools: From Roman Britain to Renaissance England. Yale University Press, 2006.
Hunt, Tony. Teaching and Learning Latin in Thirteenth-Century England. Boydell & Brewer, 1991.
Wallace, David, ed. The Cambridge History of Medieval English Literature. Cambridge University Press, 2002.
Apart from Latin works such as those mentioned above, classical texts were largely "lost" to Western Europe during the Middle Ages, due to the knowledge of Greek becoming very rare in the Latin West. In the 13th century, however, a rediscovery was just beginning to occur. Many classical texts had been translated into Arabic following the rise of Islam. Starting with the reconquest of Toledo in 1085, a large collection of such "lost" works fell into European hands. The Arabic translations were relatively easily re-translated into Latin, and in this way classical knowledge spread throughout Latin Europe again.
Of course, these were still transmitted in Latin. So if any text on Greek mythology reached 13th century England in this way, literacy in Latin would still be required to understand it first hand.
The Nun's Priest's Tale from Geoffrey Chaucer's Canterbury Tales:
Lo heere Andromacha, Ectores wyf,
That day that Ector sholde lese his lyf,
She dremed on the same nyght biforn […]
He wente for to fighte natheles,
But he was slayn anon of Achilles.
It would seem that Chaucer doesn't feel the need to give a lot of background on who Hector, Andromacha and Achilles are and why they're fighting.
The Iliad, the most important of Greek Mythology, in ancient times was at the center of western education. Children in Greece prior to the Roman expansion started learning with the Iliad, and the Iliad remained a prominent part of education through the Roman era into the middle ages. Not just Homer was important, but it is also my understanding that the works of Aristotle and Galen were studied as a part of medical training until the 1800s.
In western Europe in the "dark ages" literacy even among clergy was lower, but with the Renaissance there was a revival of Classical Education which according to Wikipedia was led by Petrus Ramus. Children from families that could afford it (and desired it), received such an education.
So the question is, what about England in the 1300s? What was the state of classical education, and hence knowledge of the Iliad and hence Greek mythology in general? This source mentions the Quadrivium being prevalent in Medieval Europe at that time.
So I think odds are if someone in 1300s England could read, they learned to read via some variant of classical education. And if they learned via classical education, they would know some Homer and Greek Mythology. If they could not read, odds are lower that they would know about this, or much else.
