Over the recent few decades, the evolving research-field of legged robotics has seen various mechanical and control-based developments. Inspired by biological species, a significant adaptation in modern mechanical leg designs has been the implementation of adjustable stiffness, shifting from what were previously simple linkages to more-complex variable stiffness actuators. Physiological studies previously demonstrated leg-stiffness modulation was not only a common trait in multiple biological locomotors, but also played a key role in disturbance recovery for humans. Guided by this, recent robotics research has shown that this can also be applied to legged robots to achieve similar locomotion adaptations, albeit often limited by the tuning time of leg stiffness in such circumstances. This study proposes real-time adaptive stiffness robot legs which are governed by fast-response magnetorheological fluid dampers, enabling stiffness adjustment upon a single step. Through experimental characterisation and model validation, these legs are shown to achieve a maximum stiffness shift of 114%. Enabled by real-time control during locomotion, improved performance and roll-angle stability is experimentally demonstrated for a bipedal robot test platform. Such improvement to locomotion is found through typical legged locomotion scenarios, with the platform encountering: obstacles, valleys, and coronal gradients in a comprehensive series of experiments.