Aircraft under the control of Brisbane Approach (North) in the period leading up to the occurrence included: - VH-TNG which was on left downwind at 3000 feet for a runway 01 ILS approach. - VH-CZL which was about 20 nm final for runway 01 ILS approach. - VH-JEX, a VFR aircraft out of Brisbane, heading north-west on climb to 4500 feet. - An Army helicopter transitting Approach (North) airspace south of the aerodrome. - A number of aircraft inbound from the north-west. As VH-JEX climbed, it experienced problems maintaining visual flight and required a number of clearance amendments with respect to both heading and altitude. During this process, the Approach (North) controller became aware of another aircraft, VH-CFQ orbiting Archerfield at 1000 feet awaiting clearance into Approach (North) airspace. The controller involved said that he was not sure how long VH-CFQ had been airborne at Archerfield but was aware of feeling under some pressure to issue a clearance. He cleared VH-CFQ to enter controlled airspace on climb to 3000 feet west of the Mt Coot-tha TV towers and returned his attention to VH-JEX and the inbound traffic from the north. A short time later, he looked to check the progress of VH-CFQ and saw a conflict with VH-TNG developing. He instructed both aircraft to turn left. However, this resulted in VH-TNG conflicting with VH-CZL. The controller then told VH-TNG to turn right for separation with VH-CZL. The 5 nm separation standard was infringed in both instances, the radar recording indicating the minimum distance to have been 3.5 nm each time. SIGIFICANT FACTORS: 1. Controller workload was significantly increased by the clearance amendments necessary for VH-JEX. 2. The controller felt under pressure to clear VH-CFQ from Archerfield into controlled airspace. 3. The clearance given to VH-JEX was inappropriate and led to the losses of separation.