There are several ways to read the theme of separation in Forster's work. In my mind, the most evident theme of separation is that of cultural distance between the Indians and the British. Due to colonization and the notion that Indian was occupied by the British, there is a natural separation between both cultures. Forster spends a great deal of time and text explaining that there is a fundamental difference or chasm between both cultures. It is not Kipling's "East vs. West" idea as much as it is that there is a separation of worlds between them. There are individuals who try to bridge this gulf, but it is a separation of worlds.
Another level of separation is the spiritual distance that exists between characters in the novel. One of the most complex elements in the novel is the idea of being spiritually separated from a temporal view of the universe. Certainly, Godbole, representing the Hindu faith, would speak to this. There is an idea that Indian spirituality and its notions represent a separation from this particular realm of existence. Forster does not really depict this in a stereotypical way as much as showing its impact on his characters. The cave represents this. When Adela and Aziz enter the cave recall how he describes the moment: "A match is struck and the sound creates two flames that for a moment touch and then are separated forever." This description connotes the idea that in the cave, where darkness and imperceptibility reign, there is a separation from the world and the temporal nature of it. Mrs. Moore also embodies the idea of separation, as towards the end of the work her life and eventual death indicate a distance between what is in our temporal space and what lies outside of it.
The final theme of separation is the one that exists between the ones we love. Part of what makes Forster's work so interesting and powerful is the idea that human beings possess a level of distance even in situations where they don't detect it. For example, Ronny and Adela do have feelings for one another. Yet, there is a separation between them. They share the same culture, and are immersed in the same situation as Anglos living in India, yet there is some gap, some separation between them. Aziz and Fielding, as friends, also experience a separation of sorts. Part of this is cultural, part is misunderstanding, and there is a part that seems intrinsic to their relationship. Even at the end, when the figments and fragments of their challenges have been set aside, one detects a certain level of separation that will always be a part of their dialectic Finally, Aziz and Godbole, both Indians, both a part of the same cultural fabric, have a level of separation between them. It is not that there is animosity between one another, but there is a separation where both cannot fully embrace the ideas of the other.
These are broad strokes, and you will probably have to go back to the text and find exact evidence to support it, but these applications of the separation theme are evident in Forster's work.