History and Theology
In the early church, communicants normally received both bread and wine. The manner in which these were received, however, changed gradually over the centuries. “In the patristic period the communicants received in their hands (see Cyril of Jerusalem, Mystagogic Catecheses 5:21-2). By the end of the sixth century women had come to be forbidden to receive the bread on the naked hand, and in the West worries about possible superstitious misuse of the sacrament and a growing respect for the eucharist led from around the ninth century to the practice of placing the host directly into the mouth. This manner of distributing the sacrament removed anxiety that small particles might be dropped, and any scruples about the need to purify the communicants’ fingers after communion, as had become the custom for the priest (see Ablutions).
The giving of the chalice lasted longer than receiving the euchartistic bread in to the hands. In the seventh century communion by intinction, that is, the dipping of the bread into the consecrated wine (intinctio panis) gained popularity. Forbidden in the West by the Third Council of Braga (675), it regained popularity in the eleventh century, only to be forbidden again in the thirteenth. By this time the reception of wine at communion by the laity had almost universally disappeared in the West, allegedly for fear of spillage. The development in eucharistic teaching that the entire Christ was present under either species (concomitance) was decisive in bringing it to an end. While the Council of Trent reaffirmed this doctrine, and restricted the chalice to the officiating priest, the Reformers maintained that communion under one form alone was contrary to the scriptural norm and the chalice was restored to the laity from the sixteenth century in the churches of the Reformation” 
Article 30 of the 39 Articles is entitled “Of both kinds” and states:
“The Cup of the Lord is not to be denied to the Lay-people: for both the parts of the Lord’s Sacrament, by Christ’s ordinance and commandment, ought to be ministered to all Christian men alike”.
John Baycroft, retired Anglican Bishop of Ottawa, has written very powerfully about the Eucharist in general and the symbolism of the Common cup in particular in his small booklet The Eucharistic Way. In the section on “Bread an Wine” he says:
“The cup is also important. Jesus took one cup and gave it to all of his disciples to drink. Perhaps it was the cup of Elijah from the Passover ritual as some people say, but it was certainly a single cup. He did not merely pour wine into the disciples’ individual cups and tell them to take a drink. There is a powerful challenge in this one. We are reminded of the agonizing decision that faced Jesus when he was praying before the crucifixion: ‘My Father, if it be possible, let this cup pass from me; nevertheless, not as I will, but as thou wilt. (Matthew 26:39). …. We are also reminded by the one cup that we cannot drink it alone. We drink from a common cup as a strong symbol of unity and and our willingness to accept each other. We share our love and lives as we share the cup. The implications for this for fellowship and support in the local church, for relationships between rich an poor in communities and nations, and for justice between North and South and first world and world countries are enormous. The cup of love and unity is unavoidably a cup of sacrifice”. 
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1. “Communion” by Donald Gray in The New Westminster Dictionary of Liturgy & Worship. Edited by Paul Bradshaw. Louisville: Westminster John Knox Press, 2002. p. 123.
See also “Communion in both kinds” in The Oxford Dictionary of the Christian Church. Edited by F.L. Cross. 3rd edition edited by E.A. Livingstone. Oxford: Oxford University Press, 1997. p. 386-387.2. The Eucharistic Way. John Baycroft. Toronto: Anglican Book Centre, 1981. p. 33-34.