Digital phenotyping offers a novel and cost-efficient approach for managing depression and anxiety. Previous studies, often limited to small-to-medium or specific populations, may lack generalizability. We conducted a cross-sectional analysis of data from 10,129 participants recruited from a UK-based general population between June 2020 and August 2022. Participants shared wearable (Fitbit) data and self-reported questionnaires on depression (PHQ-8), anxiety (GAD-7), and mood via a study app. We first examined the correlations between PHQ-8/GAD-7 scores and wearable-derived features, demographics, health data, and mood assessments. Subsequently, unsupervised clustering was used to identify behavioural patterns associated with depression or anxiety. Finally, we employed separate XGBoost models to predict depression and anxiety and compared the results using different subsets of features. We observed significant associations between the severity of depression and anxiety with several factors, including mood, age, gender, BMI, sleep patterns, physical activity, and heart rate. Clustering analysis revealed that participants simultaneously exhibiting lower physical activity levels and higher heart rates reported more severe symptoms. Prediction models incorporating all types of variables achieved the best performance ($R^2$=0.41, MAE=3.42 for depression; $R^2$=0.31, MAE=3.50 for anxiety) compared to those using subsets of variables. This study identified potential indicators for depression and anxiety, highlighting the utility of digital phenotyping and machine learning technologies for rapid screening of mental disorders in general populations. These findings provide robust real-world insights for future healthcare applications.