Fairlight, the common belief is that the ban on polygamy started with the Roman Catholic church. In actuality, the "ban" on polygamy pre-dates the Roman Catholic church by more than a century.
Here are some quotes from Early Church Fathers concerning polygamy (quoted from another site):
1. Justin Martyr (c.160) rebukes the Jews for allowing polygamy:
"Your imprudent and blind masters [i.e., Jewish teachers] even until this time permit each man to have four or five wives. And if anyone sees a beautiful woman and desires to have her, they quote the doings of Jacob." [ANF, vol. 1, p. 266]
2. Irenaeus (c.180) condemns the Gnostics for, among other things, polygamy:
"Others, again, following upon Basilides and Carpocrates, have introduced promiscuous intercourse and a plurality of wives..." [ANF, vol. 1, p.353]
3. Tertullian (c.207) was also explicit:
"Chapter II.-Marriage Lawful, But Not Polygamy. We do not indeed forbid the union of man and woman, blest by God as the seminary of the human race, and devised for the replenishment of the earth and the furnishing of the world, and therefore permitted, yet Singly. For Adam was the one husband of Eve, and Eve his one wife, one woman, one rib. (ANF: Tertullian, To His Wife)
4. Methodius (cf.290) was clear on the issue, arguing that it had stopped at the time of the Prophets:
"The contracting of marriage with several wives had been done away with from the times of the prophets. For we read, 'Do not go after your lusts, but refrain yourself from your appetites'...And in another place, 'Let your fountain be blessed and rejoice with the wife of thy youth.' This plainly forbids a plurality of wives." [ANF, vol. 6, p.312]
5 The Pseudo-Clementine Literature boasts about how St. Thomas taught the Parthians [i.e., an Iranian culture] to abandon polygamy:
"But I shall give a still stronger proof of the matters in hand. For, behold, scarcely seven years have yet passed since the advent of the righteous and true Prophet; and in the course of these, inert of all nations coming to Judaea, and moved both by the signs and miracles Which they saw, and by the grandeur of His doctrine, received His faith; and then going back to their own countries, they rejected the lawless rites of the Gentiles, and their incestuous marriages. In short, among the Parthians-as Thomas, who is preaching the Gospel amongst them, has written to us-not many now are addicted to polygamy; nor among the Medes do many throw their dead to dogs; nor are the Persians pleased with intercourse with their mothers, or incestuous marriages with their daughters; nor do the Susian women practise the adulteries that were allowed them; nor has Genesis been able to force those into crimes whom the teaching of religion restrained. (ANF 8: "Book IX: Chapter XXIX.-The Gospel More Powerful Than 'Genesis.'"]
6. The Council of Neocaesarea a.d. 315 (circa) refers to a 'purification period' for polygamists. By that time, sinners had to 'sit out' of Church activities until they had demonstrated reformation. If a sin showed up on this list of canons, it was considered a 'bad sin'--and polygamy shows up here:
"Ancient Epitome of Canon III. The time (for doing penance and purification) of polygamists is well known. A zeal for penance may shorten it." [ANF]
7. Basil, Archbishop of Caesarea, mentioned it a number of times in his letters, generally concerning the period for exclusion from church for polygamists, calling it 'limited fornication'(!):
"IV. In the case of trigamy and polygamy they laid down the same rule, in proportion, as in the case of digamy; namely one year for digamy (some authorities say two years); for trigamy men are separated for three and often for four years; but this is no longer described as marriage at all, but as polygamy; nay rather as limited fornication. It is for this reason that the Lord said to the woman of Samaria, who had five husbands, "he whom thou now hast is not thy husband." He does not reckon those who had exceeded the limits of a second marriage as worthy of the title of husband or wife. In cases of trigamy we have accepted a seclusion of five years, not by the canons, but following the precept of our predecessors. Such offenders ought not to be altogether prohibited from the privileges of the Church; they should be considered deserving of hearing after two or three years, and afterwards of being permitted to stand in their place; but they must be kept from the communion of the good gift, and only restored to the place of communion after showing some fruit of repentance. [ANF: (Canonica Prima.)To Amphilochius, concerning the Canons. Letter CLXXXVIII written c.347.]
Now the term "ban" has many meanings. There can be "official" bans, and there can be bans by acclamation. In this case, polygamy was "banned" by the prevailing view of the church. The influence of these church fathers on the practices of the church were tremendous. They were viewed as the successors, in many cases, of the apostolic teachings. While they got many of those doctrines wrong, the church tended to revere their teachings in its practice.
However, throughout history there have been portions of the church that have not banned polygamy. Many African churches, for example, appear to have had an unbroken tradition of polygamy throughout their history.
The Roman Catholic Church did issue "universal" bans upon polygamy--to Roman Catholics. Of course it had little or no effect on churches outside of Roman Catholicism.
The primary "ban" on polygamy has occurred due to the prevalent interpretation of certain portions of Scripture, derived from the Early Church Fathers like the ones above, which look at the relationship of Adam and Eve, and draw the logically fallacious argument that God "intended" men to have one wife--despite Scriptural and natural evidence to the contrary.
When was the "ban" upon polygamy? The Early Church Fathers started it due to a confused and contradictory interpretation of Scripture. Alternatively, we can state quite accurately that there never was a ban upon polygamy, but that such a ban is an EXTRA-Biblical doctrine that has persisted due to ignorance and the pressure of the majority view.
John for Christ