Vivisection, or operating on living animals for the purposes of scientific research, has a long history in medicine. It is still practiced today, in part as an alternative to experimenting on people.
Before the publication of Darwin's theory of evolution, animal experimentation was more or less tolerated in England and other countries. Very few people considered animals as anything but inferior species, so anti-cruelty legislation was all but absent. But once Darwin's theory broke down the barrier between human and animal in the popular mind, many people felt a stronger connection to the "lesser creatures." The idea that there might be unbroken lines of descent connecting species to common ancestors ultimately served to humanize the animals (at least, the ones that seemed most human to begin with). Protests of inhumane treatment of animals became increasingly prevalent. As a result, there was something of a backlash against scientists who had been involved in vivisection.
Wells tapped into the horror and empathy generated by vivisection in his creating a story in which the main emotional weight is carried by the animals rather than the men. His story had the potential to persuade others that vivisectionists were like Moreau in their coldness to animals' pain.
The vivisection debate is part of a general debate about to what length scientists should be allowed to stretch morality in the pursuit of knowledge. Darwin himself felt quite conflicted about vivisection, and he eventually acknowledged that although the practice disgusted him, it was justifiable in the pursuit of knowledge. But Moreau's base curiosity seems to cross the line.
(Picture source: http://www.victorianweb.org/science/darwin/darwin_beard.gif.)