Continuous monitoring of oil discharges in coastal and open ocean waters using Earth Observation (EO) has undeniably contributed to diminishing their occurrence wherever a detection system was in place, such as in Europe (EMSA's CleanSeaNet) or in the United States (NOAA's OR&R). This study describes the development and testing of a semi-automated oil slick detection system tailored to the Great Barrier Reef (GBR) marine park solely based on EO data as no such service was routinely available in Australia until recently. In this study, a large, curated, historical global dataset of SAR imagery acquired by Sentinel-1 SAR, now publicly available, is used to assess classification techniques, namely an empirical approach and a deep learning model, to discriminate between oil-like features and look-alikes in the scenes acquired over the marine park. An evaluation of this detection system on 10 Sentinel-1 SAR images of the GBR using two performance metrics - the detection accuracy and the false-positive rate (FPR) - shows that the classifiers perform best when combined (accuracy >98 %; FPR 0.01) rather than when used separately. This study demonstrates the benefit of sequentially combining classifiers to improve the detection and monitoring of unreported oil discharge events in SAR imagery. The workflow has also been tested outside the GBR, demonstrating its robustness when applied to other regions such as Australia's Northwest Shelf, Southeast Asia and the Pacific.