I haven't watched the movie, but from listening to the episode, I think seanotron is on the right track, Spice World is a Doctor-Who-spin-off, but not because of Richard E. Grant.
For introduction: Doctor Who is a british series about a time-travelling alien, whos space-time-transporter (TARDIS) looks like a british police box, is bigger on the inside and can telepathically translate any language. The Doctor also can regenerate, which means instead of dying he gets a new appearance.
In the Doctor-Who-books and audio plays, there is a character called Iris Wildthyme, who got her own book/audio-play-series and is more or less a parody of the Doctor. Her TARDIS looks like a british doppel-decker-bus, but is smaller on the inside.
So I guess what happened was this: Iris regenerated into a young girl, fixed the bus so it became bigger on the inside, decided to become a member of a girl group, so she recruited the other four Spice Girls as companions, the fifth Spice Girl is actually Iris herself.
This explains the bus, that they can understand the aliens and the bonker story, which fits with the adventueres, Iris normally has.
It leaves the question, which Spice Girl is actually a time-travelling alien? One candidate is the Spice Girl (don't remember, which one it was) that snogged the alien. But maybe there is another possible candidate: If I understood correctly, Baby Spice got a lot of stuffed toys in her bed? Is there maybe a stuffed panda amongst them? Because in the audio-plays, one of Iris companions is a talking stuffed panda.