All of the recurring characters are timelords - two of them, to be exact.Someone had to start a WMG for this. And in this case, it's entirely plausible.
The Fall plunged the Earth into Waterworld.In the film, we know very little about what happened to the world between the 5th and 6th (chronologically) periods depicted. The rising water levels could have led to humanity's descent into a largely water-dwelling remnant, leading in turn to the fractured cultures depicted in the final period visited.
The film is set in the same continuity as The Matrix.Specifically, it's one of the previous versions of the Matrix mentioned by the Architect in The Matrix Reloaded. The different time periods are the only time periods that version of the Matrix simulates, so its total runtime still amounts to 100 years. Sonmi is the One and her time period corresponds to a simulation of the rise of 01 as narrated in The Second Renaissance (we just don't see any robot), which can be inferred from the levitating plates on the truck, which look very much like those on the Nebuchadnezzar. All different characters played by Hugo Weaving are actually one and the same: Agent Smith, or at least an earlier version of him with the same physical features.
Frobisher and Sixsmith's brothers served together in the Great WarThey joined up under false names in order to go to war. We see their um, adventures disguised as Deamis and Daventry in The Trench.
The end of Letters from Zedelghem caused the 'comet soul' to be split in twoBook verse only, as in the film the implications about who gets reincarnated as whom are different: Frobisher's suicide could be seen as interrupting the natural birth/death/rebirth cycle and thus have unusual consequences. It would explain why Luisa and Cavendish's lifetimes overlap despite them both having the comet birthmark that implies they are the same soul as the other protagonists. It also might explain why Cavendish feels like a step backwards in terms of characterisation from Luisa - she is a continuation of the better traits picked up during Ewing and Frobisher's lifetimes, while Cavendish is a continuation of some of the worse ones.