The interesting thing about this particular title of Mary is that it has much more to do with Jesus than it does Mary! There were those who argued that Mary should not be called "Mother of God" because she was really only the mother of his humanity, not his divinity. But this created a serious theological problem: was Jesus one "person" with two "natures" (human and divine), or was he actually two seperate persons? The Church Fathers unanimously agreed that that Jesus was one "person", and to say otherwise would be a grave error. It was the Council of Ephesus (one of the councils of the Undivided Church that the Church of England has decreed "authoritative") that finally decreed in 431 that Mary is Theotokos because her son Jesus is one person who is both God and man, divine and human.
This is the actually statement made by the Fathers at Ephesus in AD 431:
"We confess, then, our Lord Jesus Christ, the only begotten Son of God, perfect God and perfect man, of a rational soul and a body, begotten before all ages from the Father in his Godhead, the same in the last days, for us and for our salvation, born of Mary the Virgin according to his humanity, one and the same consubstantial with the Father in Godhead and consubstantial with us in humanity, for a union of two natures took place. Therefore we confess one Christ, one Son, one Lord. According to this understanding of the unconfused union, we confess the holy Virgin to be the Mother of God because God the Word took flesh and became man and from his very conception united to himself the temple he took from her"