A fundamental process for cognition is action selection: choosing a particular action out of the many possible actions available. This process is widely believed to involve the basal ganglia, and we present here a model of action selection that uses spiking neurons and is in accordance with the connectivity and neuron types found in this area. Since the parameters of the model are set by neurological data, we can produce timing predictions for different action selection situations without requiring parameter tweaking. Our results show that, while an action can be selected in 14 milliseconds (or longer for actions with similar utilities), it requires 34-44 milliseconds to go from one simple action to the next. For complex actions (whose effect involves routing information between cortical areas), 59-73 milliseconds are needed. This suggests a change to the standard cognitive modelling approach of requiring 50 milliseconds for all types of actions.