Greg, I wish I had some of the references I once had. The Germans and Spanish did a bit of mumming in the Middle Ages. These plays were based on biblical events. The origin I don't know. The Spaniards had local secular plays later, the earliest I know concern the expulsion of the Moors in 1492, and earlier in some more northerly regions of Spain. These plays came across the water are are still performed in villages in New Mexico (they arrived with the first colonists in 1580-1600); the performers are called Matachines.
In German classes we used to perform "Jedermann," a mystery play which had its origin in the Middle Ages.
The only records I know from England are 14th century; Henry the Eighth banned the practice (Malcolm would say that the ban was against disguises).

I agree that the usual performance in England is much later, since key characters such as the doctor are from the Venetian Commedia delle' Arté of Renaissance times (may have an earlier tradition in the Italian peninsula- I don't know).