In this research, we apply machine learning models to improve retail forecasting for fresh food by integrating external factors such as promotions, weather, and holidays. This study tackles the problems that often challenge real-world data, such as truncation, incompleteness, and effects from external data. We train and develop one statistical model and various machine learning models, including deep learning models, using the case study approach and real-world data from a plant-based fresh food Swedish retailer. We integrate external factors to investigate which factors influence demand the most, how they affect model accuracy, and how we can improve the models to use the external models better. The results indicate that incorporating external factors can affect the demand in the fresh-food retail industry, especially discount data, reducing waste and avoiding missed sales opportunities. This study offers significant insights into the most impactful external factors, a comparison between different models and different datasets, and the effectiveness of various machine learning techniques in forecasting demand for the fresh food retail industry.