I know that
The Land of Mist by Sir Arthur Conan Doyle, one of his sequels to The Lost World, is all about theosophy and the Spiritualist movement (it's quite a classic example of Clubbing The Reader Over The Head With A Real-World Point Of View, but still quite worth reading), and simply by reading that story I got the definite idea of multiple planes of existance, although in a 'moral sequence'.
Here's a couple of quotes from one paragraph, spoken by a spirit; Doyle died in 1930, but my copy of the story doesn't mention a precise publication date.
A. C. Doyle said:
"Children are not born here. That is only on the earth plane. [Later in the passage] ... when two high-souled lovers meet upon your plane. ..."
And other references to 'lower spheres' and so forth. So the concept of 'plane' was certainly about at that time, and the Spiritualist movement Doyle was covering was perhaps a half-century old at the time (1920s, I'd say; the story mentions soldiers, who seemed to have died in the Great War).
However, this planar structure was clearly Christian and sequential in nature. People were born on Earth, lived, and died; wherupon their mind lived on, and once it figured out what was going on and become purer, it progressed to a higher plane, of which there were seven or so known to the spirits talking through mediums (and they implied more beyond that, but they didn't know about them, implying that they're even more rarified and such than the planes after death). There were also spirits who didn't progress or were too corrupt to progress without people helping them self-improve; it's unclear whether they were on lower planes or still on this one, immaterial (or not so immaterial, in one case). A ladder, if you will, rather than the wheel or web more beloved of slightly more modern conceptualists (Moorcock was writing 30-40 years after this, an equal amount of time in our past).
So: 'plane' has been around a while, according to my meagre, fiction-filtered knowledge.