A clearance to line up on the runway had previously been given. The crew reported that after they were cleared for take off and were applying take off power a vehicle was seen approaching the runway on taxiway alpha. They observed the vehicle continue and cross the runway in front of them. The take off was rejected from a relatively low speed. A different version of events was presented by control tower staff. A clearance was given for the vehicle to cross the runway. They said that as the aircraft was on the taxiway approaching the runway it was judged that the vehicle would be clear of the runway. The Manual of Air Traffic Services allows a take off clearance to be given if, in the opinion of the controller, no collision risk exists and there is reasonable assurance that separation will exist when the aircraft commences take-off roll. A take off clearance was given under this provision when the air traffic controller assessed it was safe to do so. Although the situation may have been tighter than expected the vehicle was seen moving away from the runway when the take-off was rejected. It has not been possible to resolve the discrepancies between these two versions of the events. Significant Factors: The following factors were considered relevant to development of the incident: 1 It was not possible to assign factors to this incident.