VH-AWL was operating over the central business district (CBD) at 2000 feet when VH-AGS called Essendon tower at Point Ormond (PTO) requesting clearance also to operate over the CBD at 2000 feet. Due to workload the clearance was denied and VH-AGS was asked to sight VH-AWL. Later, a radar return was observed entering the control zone north of Point Ormond flying at the same level and in the opposite direction to VH-AWL. The pilot of VH-AGS was asked to sight VH-AWL which he did at a range of about one mile. There was insufficient time to alert VH-AWL. VH-AGS was about 1.5 miles inside the control zone at the time of the confliction. The pilot of VH-AGS later claimed that he thought he was cleared to enter the control zone once he had sighted the other aircraft. He also thought he had been told the other aircraft was at 3000 feet. He had the other aircraft in sight from the time he entered the control zone until the confliction occurred. He estimated the two aircraft passed with 200 feet of vertical separation and about 200 metres of lateral separation.