In Western communion services, when was the origin of the practice of consistently offering only the bread to the laity? The practice of "communion in both kinds" by the laity, that is, both the eating of the bread and drinking of the cup, seems to have been the typical practice in the early church.  1 Corinthians 11:28 reads:


  Let a person examine himself, then, and so eat of the bread and drink of the cup. (ESV)


And the Didache implies the taking of both kinds by baptized Christians in 9.5:


  And let none eat or drink of your Eucharist but such as have been baptized into the name of the Lord


But at some point along the way, it became normal for the laity to receive only the bread; so much so that the 15th-century Council of Constance "banned" the offering of the cup to the laity (so says Wikipedia).

That Wikipedia article associates the practice with the Middle Ages, and suggests that the transition may have begun in order to accommodate the celebration of the Eucharist away from the normal gathering place, such as in the home of a bedridden church member.

Here though I'm interested in when this became the normal, week-to-week practice in the local church.  What is the first evidence that a church in Western Christendom was consistently offering only the bread to the laity?
In Western communion services, when was the origin of the practice of consistently offering only the bread to the laity?

The answer is not so clear cut as one would imagine. One can not say that at this date in time, communion was uniquely offered to the laity under the form of bread only. In fact the practice of receiving communion under the form of bread (Body of Christ) came about little by little over several centuries.


  From the earliest times: The faithful received Communion under both species, standing. The Host was distributed in de hand but women were reguired to have a cloth over their hands to receive. 
  
  ca.590: Practice of Communion on the tongue appears but not common.
  
  Xth-XIth Century: Communion in the hand decreases and is abolished for fear of profanation.
  
  XIth-XVIth Century: Practice of kneeling to receive Communion becomes primary practice.
  
  1414: After a long decrease in reception from the chalice, practice abolished to combat Hussite heresy.
  
  1963-1970: Communion under both species restored in most cases along with option to recieve in the hand and standing.
  
  1968: Permission granted for laity to distribute Communion in extraordinary circumstances for the fist time in the history of the Church. - Source


Although communion under both kinds was the general practice in the Early Church and it lasted thus for many centuries. It took to the twelfth century for the Church to tried to suppress this practice. The Council of Lambeth (1281) stated that wine is to be received by the priest alone. The practice took time to be imposed and it is impossible to say exactly when the new custom became universal or when, by the Church's approval, it acquired the force of law. It seems the communion with the chalice may never have true vanish completely or truly universally as the Catholic Encyclopedia more or less points out.


  From the first to the twelfth century
  
  It may be stated as a general fact, that down to the twelfth century, in the West as well as in the East, public Communion in the churches was ordinarily administered and received under both kinds. That such was the practice in Apostolic times is implied in 1 Corinthians 11:28 (see above), nor does the abbreviated reference to the "breaking of bread" in the Acts of the Apostles (ii, 46) prove anything to the contrary. The witness to the same effect for the sub-Apostolic and subsequent ages are too numerous, and the fact itself too clearly beyond dispute, to require that the evidence should be cited here. But side by side with the regular liturgical usage of Communion sub utraque, there existed from the earlist times the custom of communicating in certain cases under one kind alone. This custom is exemplified (1) in the not infrequent practice of private domestic Communion, portion of the Eucharistic bread being brought by the faithful to their homes and there reserved for this purpose; (2) in the Communion of the sick, which was usually administered under the species of bread alone; (3) in the Communion of children which was usually given, even in the churches, under the species of wine alone, but sometimes under the species of bread alone; (4) in the Communion under the species of bread alone at the Mass of the Presanctified, and as an optional practice, in some churches on ordinary occasions. To these examples may be added (5) the practice of the intinctio panis, i.e. the dipping of the consecrated bread in the Precious Blood and its administration per modum cibi. We will notice briefly the history of each of these divergent practices.
  
  Since the twelfth century
  
  The final suppression of intinctio was followed in the thirteenth century by the gradual abolition for the laity of Communion under the species of wine. The desuetude of the chalice was not yet universal in St. Thomas' time (d. 1274): "provide in quibusdam ecclesiis observatur", he says "ut populo sanguis sumendus non detur, sed solum a sacerdote sumatur" (Summa, III, Q. lxxx, a. 12). The Council of Lambeth (1281) directs that wine is to be received by the priest alone, and non-consecrated wine is to be received by the faithful (Mansi, XXIV, 405). It is impossible to say exactly when the new custom became universal or when, by the Church's approval, it acquired the force of law. But such was already the case long the outbreak of the Hussite disturbances, as is clear from the decree of the Council of Constance (see I above). The Council of Basle granted (1433) the use of the chalice to the Calixtines of Bohemia under certain conditions, the chief of which was acknowledgment of Christ's integral presence under either kind. This concession, which had never been approved by any pope, was positively revoked in 1462 by the Nuncio Fantini on the order of Pius II. The Council of Trent while defining the points already mentioned, referred to the pope the decision of the question whether the urgent petition of the German emperor to have the use of the chalice allowed in his dominions be granted; and in 1564 Pius IV authorized some German bishops to permit it in their dioceses, provided certain conditions were fulfilled. But, owing to the inconveniences that were found to result, this concession was withdrawn in the following year. Benedict XIV states (De Missae Sacrif. II, xxii. n. 32) that in his time the kings of France had the privilege of communicating sub utraque at their coronation and on their death-bed. In the eighteenth century the deacon and subdeacon officiating at High Mass in the Church of Saint-Denis, Paris, on Sundays and solemn feasts, and at Cluny on all feasts of obligation, were allowed to receive sub utraque (Benedict XIV, loc. cit.) The only surviving example of this privilege is in the case of the deacon and subdeacon officiating in the solemn Mass of the pope.