I believe that Kirkup is using the word "uniforms" as a metaphor for all the things that we "put on" to make ourselves different from other people of the world. These are especially necessary during wars because war is the time when we are most trying to differentiate ourselves from other people.
In this poem, Kirkup is trying to say that people are all essentially the same. But, he says, we put on these "uniforms" to make ourselves seem different. We call ourself Christian or Muslim, we support one cricket team or football team or whatever other kind of team. We see ourselves as American or English or Chinese. We seem to have an innate tendency to do this.
In war, it is especially important to tell one side from the other. War is the time when we are trying hardest to be different. In war we are saying that our kinds of people are so different that we must kill each other. When we do this, we must be sure that we are making ourselves be as different as possible because we would not want to kill if we thought the other people were just like us.