VH-TEQ was conducting circuits and was instructed to report when ready to turn base for runway 12. VH-TAK was on approach for runway 35. The aerodrome controller (ADC) was under training and when the pilot of VH-TEQ reported ready for base he elected to make that aircraft number one in the landing sequence. He instructed VH-TEQ to make a short approach and then cleared that aircraft for a touch-and-go with a request to expedite crossing the runway intersection. The pilot of VH-TEQ attempted to carry out these instructions to the best of his ability but did not perform as speedily as the ADC expected. The rated controller observed this action and decided that the runway separation standard would exist by the time VH-TAK needed a landing clearance. The crew of VH-TAK were twice told by the ADC to expect a late landing clearance and the captain elected to continue his approach as he could see that the runway was clear and air traffic control had given him a landing expectancy. Although realising that another aircraft was on a crossing runway and conducting a lookout, the crew of VH-TAK did not see VH-TEQ until after touch down. Traffic information was not passed to either crew. When the ADC trainee and training officer realised that the runway separation standard may be infringed, they considered that the safest action was to land VH-TAK as VH-TEQ had commenced rotation from the touch-and-go. A landing clearance was issued to VH-TAK as that aircraft approached the threshold. When VH-TAK was on its landing roll, VH-TEQ crossed the runway intersection at a height of approximately 100-150 ft. As a result the required landing separation had not been maintained. Significant Factor The following factors were considered relevant to the development of this incident: 1.The ADC trainee misjudged the traffic situation. 2.The ADC training officer did not take sufficient action early enough to prevent a breakdown in separation standards. 3.Traffic information was not given to either crew.