The Time Machine presents two very different settings – the 1890s and the distant future – and seems to dare us to make connections between them. When the Time Traveller jumps into the far future, he finds a society where the Eloi play all day and don't do any work. It's almost like an episode of Gossip Girl, where (almost) everyone is pretty and rich. In other words, it looks much better than the Time Traveller's own time, which is full of conflict and anxiety over the issue of class – who has to do work and who gets to profit from the work of others. (This is a big issue in the 19th century; check out "Setting" for more on this.)
However, the future stops looking good to the Time Traveller when he realizes that the class conflict and class structure of his time have merely evolved rather than being erased. Although some aspects of social class have changed, there are many similarities that should make us sit up and take notice. (For instance, in both cases, the working class tends to be invisible or hard to find.) So while the future might look like an exaggeration of the 19th century (no one is literally eating each other in Britain in the 1890s), the novel is making a suggestion about where humans are heading.
The Time Traveller spends most of his time working through the evolution of social class because that's the theme his readers would be most interested in.
Even though The Time Machine tells a story about working-class oppression, it makes us identify more with the upper class: the Time Traveller and the Eloi.