T. S. Eliot's play Murder in the Cathedral is based on an actual historical event, the murder of Thomas Beckett, Archbishop of Canterbury, on December 29, 1170, in Canterbury Cathedral, probably at the instigation of King Henry II.
In the twelfth century, Roman Catholicism was the official religion of England. In the events of Murder in the Cathedral, we see the beginnings of the tension that would eventually lead King Henry VIII in 1534 to separate the Church of England from that of Rome. In the twelfth century, however, there was no talk of spiritual independence from Rome, but rather a dispute over power within the structure of Roman Catholicism.
The dispute originates in the problem of "church temporalities," the properties owned by the church. Under the feudal system, all land belongs to the king and is assigned to vassals (the various noblemen who in practice own and run estates) in return for their service. The Roman Catholic monasteries and cathedrals owned vast tracts of land and enjoyed considerable wealth. This leads to a conflict. Even though the Pope as head of the church has ultimate say in spiritual matters, in temporal matters, the king had absolute authority. Thus, Henry II felt that he should be able to select bishops and have some control of the revenue deriving from church property on English soil; Thomas Beckett supported the Papal position that church temporalities should be controlled by Rome.
Further complicating this issue was that the Pope, as well as being a religious authority, also was the temporal ruler of the Papal States (a small territory in Italy) and as such acted as a secular head of state as well as a religious figure. In this dual identity, the Pope tended to ally with enemies of England, leading Henry II to have additional qualms about bishops selected by the Pope.
Thus even though Eliot's play focuses on the moral dilemma's of Thomas Beckett, the background involves practical conflicts over church power and property.