Fever Crumb

Fever Crumb is set in a futuristic post-apocalyptic London. Population is now less than 100,000. A group of people that view themselves as homo-superiorous had ruled the city. However, due in part to lack of reproduction, they had been killed off by the local population. The book focuses on a group of "engineers" that work to support science regardless of who is in power. They stress rationale thought above all else, and try to avoid personal superstition and human relations. One day, however, a little girl appears on their doorstep. She is somewhat "different" with miscolored eyes. Dr. Crumb takes her in and raises her as a fully rational engineer. At 14, she is sent out to help with an archaeological site. In the process, she runs into some people that think she is one of the previous rulers. An old hunter and boy try to hunt her down, providing the drama. Eventually, new rulers come into London, with plans for moving cities. They discover Fever's parentage and Fever decides she wants to be out on her own.
The world is an interesting future that discovers bits and pieces of today's world, but obviously still has a large technological gap. Fever is a very sympathetic character. She is trying to find her way in the world after her very rationalistic upbringing. You can see how this can turn into a large number of future stories.