For the most part , the campaign was fought between the forces of the Italian Royal Navy ( Regia Marina ) , supported by other Axis naval forces , and the forces of the British Royal Navy , supported by other Allied naval forces . For the most part , the campaign was fought between the Italian Royal Navy ( Regia Marina ) , supported by other Axis naval and air forces , and the British Royal Navy , supported by other Allied naval forces , such as Australia , Netherlands , Poland and Greece .