Did Winston Churchill believe in God?

no, Churchill did not have any religious views. (Wrong)

Yes and no. Churchill believed in a sort of Divine providence or God but was very critical of over zealous religion and dogmatism. He was a deist at most. He believed in an afterlife (He claimed to have encountered Abraham Lincoln's ghost while staying at the white house) and often alluded to God in his speeches.
"I have nothing to offer but blood, toil, tears and sweat…. You ask what is our policy? I will say: It is to wage war by sea, land and air with all our might and with all the strength that God can give us: to wage war against a monstrous tyranny, never surpassed in the dark, lamentable catalogue of human crime. That is our policy. You ask what is our aim? I can answer in one word: Victory, victory at all costs, victory in spite of all terror, victory, however long and hard the road will be; for without victory, there is no survival."

"Which way shall we turn to save out lives and the future of the world? It does not matter so much for old people: they are going soon away; but I find it poignant to look at youth in all its activity and ardour…and wonder what would lie before them if God wearied of mankind"