The brain has a great capacity for computation and efficient resolution of complex problems, far surpassing modern computers. Neuromorphic engineering seeks to mimic the basic principles of the brain to develop systems capable of achieving such capabilities. In the neuromorphic field, navigation systems are of great interest due to their potential applicability to robotics, although these systems are still a challenge to be solved. This work proposes a spike-based robotic navigation and environment pseudomapping system formed by a bio-inspired hippocampal memory model connected to a Posterior Parietal Cortex model. The hippocampus is in charge of maintaining a representation of an environment state map, and the PPC is in charge of local decision-making. This system was implemented on the SpiNNaker hardware platform using Spiking Neural Networks. A set of real-time experiments was applied to demonstrate the correct functioning of the system in virtual and physical environments on a robotic platform. The system is able to navigate through the environment to reach a goal position starting from an initial position, avoiding obstacles and mapping the environment. To the best of the authors knowledge, this is the first implementation of an environment pseudo-mapping system with dynamic learning based on a bio-inspired hippocampal memory.