I woke up the other morning with this story on my mind. I've tried some googling, but my efforts are coming up with nothing useful. My memory of the specifics of the material is pretty pathetic, apologies.
What it was: A novella, novel, or series of novels
When I read it/When it was written: I read it between 2000 and 2010; it would have been written no more than 10 years earlier.
A group of modern or near future men and women are transported instantaneously to a strange planet by means I can't remember. It may have been your typical "glowing ball of mysterious light", but I'm not certain. All future activities occur either on that world or on a shifting series of closely related worlds.
Upon arrival they find wilderness and eventually, while evading Earth-like jungle terrors, they stumble on an encampment of Victorian era Brits. The Victorians are very much "Dr. Livingston, I presume." types, and we find that they were zapped out of 1800's England in much the same way. The Victorians (if I recall correctly) keep a Neanderthal or Australopithecene as "servants" and are doing their best to preserve their version of civilization against the barbaric surroundings they've been forced into. They clearly arrived well before the main characters, but if I recall correctly, they did not arrive 200+ years before, more like 20.
Eventually we meet some slavers who may have been pirates before being taken. I think that they enslave one of the main characters for a period of time before he is rescued. There may be some weird religious imagery at this point in the story as well.
The most bizarre bit of the book involves the eventual encounter of the main characters with an extremely advanced race of hominids who have evolved from a completely different ancestor, perhaps Gigantopithecus. They are huge, gorilla-like people who are peaceful and have technology that is way beyond our lineage.
At one point in the story the humans, perhaps with the help of the Gigantopithecuses, look through what is essentially a catalogue of possible Earths. They see dozens of different planets, each of which has a slightly different timeline, before moving on to some with wildly different histories, like an Earth that has become completely engulfed in ice, from which the Neanderthals come. This might have been the explanation for all of the people from various time periods arriving at nearly the same time on the story's Earth.
The next bit is spoilered to avoid giving away the ending:
The main characters and the Gigantopithecus and Neanderthal who have teamed up with them figure out how to manipulate a forcefield protected computer/crystal/teleporter thing of mysterious origin in order to send them home (or perhaps just stop more people from being zapped to this place.) The Gigantopithecus makes a deal with the main characters, they achieve their goal. The humans had, at one point, promised the Neanderthal that they would help get it home. The Gigantopithecus understands that to be an unbreakable contract (it cannot lie) and so the price of its help winds up being transportation of the Neanderthal, along with an unwilling human companion (a woman who has been unpleasant throughout the story, if I remember right) back to the ice world from which the Neanderthal had come.