Remote sensing technology using synthetic aperture radar (SAR) images is the most effective technique for ocean oil spill surveillance in the hot spot regions like surroundings of oil platforms, oil rigs and major ship traffic routes to help protect the ocean ecosystem. A framework for the detection and quantification of daily oil pollution in the ocean is presented and explained in detail. This paper describes a new approach to SAR oil spill detection using bag of visual words (BOVW) method of feature extraction and classification. A labelled dataset of verified oil spills and look-alikes with the aid of Marios Krestenitis is used for demonstrating the use of BOVW method for feature extraction and classification of oil spills and look-alikes. The overall accuracy of 93% is obtained for the classification of oil spills and look-alikes from SAR images. An analysis of the BOVW method of feature extraction and classification in this paper has highlighted the importance of speeded-up robust features (SURF) features used by the algorithm for accurately classifying the oil spills and look-alikes. Fixed oil platforms and major ship traffic routes in the Eastern Arabian Sea are selected for oil spill surveillance. Initially, detection and quantification of some reported oil spills in the year 2017 is performed for validation. Subsequently, the technique is implemented for unreported oil spills from January to November 2020 to investigate the occurrence of oil spill incidents from oil fields and ships in the selected study region.