A Boeing 747-338 aircraft VH-EBU was inbound to Cairns on the 153 Very High Frequency (VHF) Omni-Directional Range (VOR) radial and had been assigned 3000 feet not below the DME steps. The pilot reported visual at approximately 15 NM south of Cairns, and was then cleared to track for a left base for runway 15. VH-XFW an Embraer EMB-120ER was departing Cairns runway 15 for Bamaga and was given a departure instruction to turn left onto a heading of 030 degrees magnetic and to maintain 2000 ft. VH-EBU was observed by radar to descend below 3000 ft. The approach controller instructed VH-XFW to maintain 1500 ft and VH-EBU to maintain 2500 ft. The pilot of VH-EBU said it was too late and that he had the other aircraft in sight to his right. VH-EBU was then cleared for a visual approach and instructed to call the tower. VH-XFW was given climb and tracking instructions to intercept the outbound track. Examination of the Automatic Voice Recording (AVR) tape and the radar tape showed that at 0119:20 EST the minimum horizontal separation was 1.33 NM and the vertical separation was approximately 600 ft. The minimum separation standards are 3 NM and 1000 feet. Interview with the crew of VH-EBU indicated that when VH-EBU was cleared to track for a left base for runway 15 (after reporting visual) it was assumed that they had been cleared for a visual approach. Accordingly, a descent to 1500 ft was initiated, which is circuit altitude. The crew of VH-EBU had not been cleared for a visual approach however, and thus had not been cleared to descend below 3000 ft. Safety Action. The crew of VH-EBU have been counselled as to visual approach requirements, and a notice to pilots will be issued to prevent a recurrence.