The phrase, as referenced by Lewis, goes back to 1680 in a work called Church History of the Government of Bishops by Richard Baxter (1615-91), a Puritan. In this work, Baxter wrote:
I am a Christian, a Mere Christian, of no other Religion; and the Church that I am of is the Christian Church ... But must you know what Sect or Party I am of? I am against all Sects and dividing Parties ...
Lewis sought deliberately to stay within the bounds of "mere Christianity" in his writings. As he wrote in the preface to Mere Christianity, "Ever since I became a Christian I have thought that the best, perhaps the only, service I could do for my unbelieving neighbours was to explain and defend the belief that has become common to nearly all Christians at all times."
Lewis likened "mere Christianity" to a hall with various doors leading to different rooms. Douglas Gresham, stepson of C.S. Lewis, once explained to me that Lewis had in mind the great hall of a home, perhaps something like Americans might think of as a living room, with doors leading to other rooms. In other words, Lewis did not have in mind a typical hallway. Thus Lewis writes, "If I can bring anyone into that hall I shall have done what I attempted."
In a BBC broadcast that first aired in January 1942, Lewis spoke the following words on the air, but they were omitted from the later printed version:
One thing I can promise you. In spite of all the unfortunate differences between Christians, what they agree on is still something pretty big and pretty solid: big enough to blow any of us sky-high if it happens to be true. And if it's true, it's quite ridiculous to put off doing anything about it simply because Christians don't fully agree among themselves. [cited in C.S. Lewis: Companion & Guide, p. 307]
In other words, throughout the centuries, Christians have always agreed on a core set of essential beliefs. There are differences, to be sure, which of course result in different Christian traditions and denominational squabbling, but the core remains and it is crucial.