It's worth noting that even before Everett the prospect of multiverses was raised in 'serious' physics by the Einstein-Rosen Bridge concept, wherein wormholes would connect our universe to parallel universes.
I need to review that, AntiGuv. Were the Einstein-Rosen bridges thought (by Einstein and Rosen and others) to connect parallel universes? Or just different parts of our own universe? (I tend to think it's the latter, but I haven't checked.)
Well, the hypothetical Einstein-Rosen bridges are, to day, a speculative concept, but so far as the equations go then it could be either. In short, wormholes could connect either different parts of our own universe or connect our universe to a parallel universe. It hardly means that parallel universes do exist; it just means that parallel universes do not at all contradict General Relativity. Einstein recognized this.