The utilisation of foundation models as smartphone assistants, termed app agents, is a critical research challenge. These agents aim to execute human instructions on smartphones by interpreting textual instructions and performing actions via the device's interface. While promising, current approaches face significant limitations. Methods that use large proprietary models, such as GPT-4o, are computationally expensive, while those that use smaller fine-tuned models often lack adaptability to out-of-distribution tasks. In this work, we introduce AppVLM, a lightweight Vision-Language Model (VLM). First, we fine-tune it offline on the AndroidControl dataset. Then, we refine its policy by collecting data from the AndroidWorld environment and performing further training iterations. Our results indicate that AppVLM achieves the highest action prediction accuracy in offline evaluation on the AndroidControl dataset, compared to all evaluated baselines, and matches GPT-4o in online task completion success rate in the AndroidWorld environment, while being up to ten times faster. This makes AppVLM a practical and efficient solution for real-world deployment.