Vision-and-Language Navigation in Continuous Environments (VLN-CE) requires agents to execute sequential navigation actions in complex environments guided by natural language instructions. Current approaches often struggle with generalizing to novel environments and adapting to ongoing changes during navigation. Inspired by human cognition, we present NavMorph, a self-evolving world model framework that enhances environmental understanding and decision-making in VLN-CE tasks. NavMorph employs compact latent representations to model environmental dynamics, equipping agents with foresight for adaptive planning and policy refinement. By integrating a novel Contextual Evolution Memory, NavMorph leverages scene-contextual information to support effective navigation while maintaining online adaptability. Extensive experiments demonstrate that our method achieves notable performance improvements on popular VLN-CE benchmarks. Code is available in the Supplementary Material.