VH-ANP, inbound from the north was being processed for a runway 26 ILS approach to Essendon. VH-EAJ, also inbound from the north, was being processed for a runway 27 ILS approach to Melbourne. While tracking in an easterly direction, on a right downwind leg for the ILS approach, the pilot of ANP reported he had Essendon in sight. He then requested priority as a Med 1 flight for clearance direct to Essendon.
To facilitate separation with, and priority for, ANP, EAJ was instructed to climb to and maintain 4,000 ft. Shortly afterwards, when in the Epping area, and maintaining 4,000 ft, EAJ was instructed to turn right heading 310 deg for a vectored right orbit. At this time, ANP was to the east of EAJ, on a southerly heading, on descent to 2,500 ft, on a wide right base for runway 26 and with the mode C level indicating 3200 ft. There was a strong westerly wind blowing above 2,000 ft and this resulted EAJ making good a track of approximately 335 deg from a heading of 310 deg.
The two aircraft passed with less than three miles horizontal separation when vertical separation was 800 ft. The pilot of ANP had EAJ in sight.