Data collection in imitation learning often requires significant, laborious human supervision, such as numerous demonstrations, and/or frequent environment resets for methods that incorporate reinforcement learning. In this work, we propose an alternative approach, MILES: a fully autonomous, self-supervised data collection paradigm, and we show that this enables efficient policy learning from just a single demonstration and a single environment reset. MILES autonomously learns a policy for returning to and then following the single demonstration, whilst being self-guided during data collection, eliminating the need for additional human interventions. We evaluated MILES across several real-world tasks, including tasks that require precise contact-rich manipulation such as locking a lock with a key. We found that, under the constraints of a single demonstration and no repeated environment resetting, MILES significantly outperforms state-of-the-art alternatives like imitation learning methods that leverage reinforcement learning. Videos of our experiments and code can be found on our webpage: www.robot-learning.uk/miles.