Apart from the obvious answer that the main character in The War of the Worlds is the narrator, we can look beyond him personally to discover a deeper meaning in Wells's sci-fi/dystopian fable. One could argue that the real central character or protagonist is humanity as a whole.
Wells presents in terrifying detail a series of episodes in the invasion of earth by aliens. Through most of the story the center of the action is the narrator himself, but there are also long sections in which he relates the experiences his brother separately had during the same period. From the apocalyptic nature of the alien attack, in which both the "heat ray" and the "black smoke" (poison gas) are used, it's obvious that mankind, the protagonist, has no chance alone against the Martians. So a third party, so to speak, is Nature, in the form of bacteria which the aliens succumb to, is the decisive factor in the struggle. The narrator himself is one of millions who manage to survive, and his personal story is one of many. The close of the novel, in which he discovers his wife, whom he had believed dead, is also a survivor seems almost an afterthought.
An interesting point is that, as discussed extensively by Isaac Asimov, it is apparently only Britain that has been attacked by the aliens. We are told that relief supplies begin pouring in from the rest of the world, which has, far as we can tell, been spared the Martian onslaught. One wonders if Wells meant specifically the British people to be the collective protagonist of the story. If so, does this support or refute the interpretation (which I tend to disagree with myself) of The War of the Worlds as an allegory of European, or specifically British, imperialism against the other continents? Or could it even be a form of satire, possibly unconscious: an attack on the notion that the sun rises and sets on Britain alone? In any event, Wells was not a nationalistic ideologue himself. If anything he was the opposite, critical of the chauvinism of his time, and it seems likely to me that he intended the story chiefly as a parable of the vulnerability of mankind as a whole.