The Chronicles of Narnia & Christianity

I've heard most sects of Christianity claim that The Chronicles of Narnia are a Christian allegory. I have no problem with this. In fact, it always fascinates me that so many different churches quote C.S. Lewis. I was however curious as to whether this is what C.S. Lewis intended. I found this quote at wikipedia from Of Other Worlds

Some people seem to think that I began by asking myself how I could say something about Christianity to children; then fixed on the fairy tale as an instrument, then collected information about child psychology and decided what age group I’d write for; then drew up a list of basic Christian truths and hammered out ‘allegories’ to embody them. This is all pure moonshine. I couldn’t write in that way. It all began with images; a faun carrying an umbrella, a queen on a sledge, a magnificent lion. At first there wasn’t anything Christian about them; that element pushed itself in of its own accord.