When I read this poem I'm reminded of John Donne's "Meditation XVII."  The world is interconnected in more ways than it ever has been before.  We can see and hear and do business across the world instantaneously, and the relative ease of travel and communication has helped all cultures intermingle in ways that were never possible before.  What happens in one place has ripple effects in another, and we must recognize our interdependence.  John Donne said it this way:

"All mankind is of one author, and is one volume; when one man dies, one chapter is not torn out of the book, but translated into a better language.... No man is an island, entire of itself...any man's death diminishes me, because I am involved in mankind; and therefore never send to know for whom the bell tolls; it tolls for thee."

In death and in life--and especially in the looming shadow of nuclear weapons--the need for the hour is recognizing that we're more alike than different, and we're all of one race...the human race. 

I assume that when you say "need of the hour" you mean the thing that is most important in the world today.  If that is the meaning, my answer is that what we need most is understanding and good will between people.  This is more important than ever given that we have nuclear weapons that can kill millions of people very easily.

This idea is reflected in Kirkup's poem.  He is making a plea for all people to see that they are similar to one another.  It would be a call, for example, for people in Pakistan and India to realize that they share hopes and fears and are, essentially, the same.  The hope is that, if they realize this, they will not want to attack each other, possibly with nuclear weapons.

In today's world with our ability to kill one another so efficiently, it is very important to (as Kirkup hopes we will) recognize our common humanity so we will not want to kill one another.