The Argo programme has transformed ocean monitoring, deploying over 4,000 floats for climate modelling and ocean forecasting. However, quality control remains a significant challenge as Real-Time Quality Control often misses subtle issues, and Delayed-Mode Quality Control is time-consuming, delaying validated datasets by over a year. Erroneous profiles can distort climate analyses. This paper introduces Hybrid Anomaly Detection - Quality Control (HAD-QC), a novel framework combining machine learning with existing Argo QC rules to enhance accuracy and scalability. HAD-QC integrates an autoencoder for unsupervised anomaly detection, a supervised ensemble classifier and 18 traditional Argo QC tests, with outputs fused via a weighting scheme. Tested on 3,200 Argo float profiles across different ocean basins, HAD-QC substantially improves anomaly finding, outperforming Real-Time Quality Control significantly. It achieved an F1-score of 90.4%, an 87% anomaly detection rate and 93% overall accuracy, overall a better performance compared with current approach to Real-Time Quality Control. HAD-QC is designed for compatibility with Argo Data Assembly Center pipelines, offering interpretability and traceability of Quality Control decisions, and is extensible to emerging Deep and Biogeochemical Argo missions.