Imitation learning has unlocked the potential for robots to exhibit highly dexterous behaviours. However, it still struggles with long-horizon, multi-object tasks due to poor sample efficiency and limited generalisation. Existing methods require a substantial number of demonstrations to cover possible task variations, making them costly and often impractical for real-world deployment. We address this challenge by introducing oriented affordance frames, a structured representation for state and action spaces that improves spatial and intra-category generalisation and enables policies to be learned efficiently from only 10 demonstrations. More importantly, we show how this abstraction allows for compositional generalisation of independently trained sub-policies to solve long-horizon, multi-object tasks. To seamlessly transition between sub-policies, we introduce the notion of self-progress prediction, which we directly derive from the duration of the training demonstrations. We validate our method across three real-world tasks, each requiring multi-step, multi-object interactions. Despite the small dataset, our policies generalise robustly to unseen object appearances, geometries, and spatial arrangements, achieving high success rates without reliance on exhaustive training data. Video demonstration can be found on our project page: https://affordance-policy.github.io/.