Murder in the Cathedral is a work of political protest. George Bell, the politically active Bishop of Chichester, commissioned T. S. Eliot to write the play to protest events in Nazi Germany, particularly the Night of the Long Knives in which Hitler lawlessly purged his party by having more than 85 people assassinated including his close friend Ernst Röhm. This event, in which Hitler acted outside of the law, was a turning point that convinced many people that Hitler was not going to "adjust" and learn to behave in a civilized way.
The major event of the play, King Henry II's decision to have Thomas Becket, the Archbishop of Canterbury, assassinated in 1170, has parallels with the Night of the Long Knives. In both cases, a powerful ruler has a former friend who has become a political liability assassinated in an act that is completely outside of the law. In both cases, despite an outcry or slaps on the wrist, the leader gets away with the murder.
The play was written to encourage people to speak out against Hitler's tyranny rather than accept it passively. Eliot used the play to show that Becket resisted the same temptations to collaborating with evil that still tempted people in the 1930s to do the same.