We present a biologically inspired sound localisation system for reverberant environments using the Cascade of Asymmetric Resonators with Fast-Acting Compression (CAR-FAC) cochlear model. The system exploits a CAR-FAC pair to pre-process binaural signals that travel through the inherent delay line of the cascade structures, as each filter acts as a delay unit. Following the filtering, each cochlear channel is cross-correlated with all the channels of the other cochlea using a quantised instantaneous correlation function to form a 2-D instantaneous correlation matrix (correlogram). The correlogram contains both interaural time difference and spectral information. The generated correlograms are analysed using a regression neural network for localisation. We investigate the effect of the CAR-FAC nonlinearity on the system performance by comparing it with a CAR only version. To verify that the CAR/CAR-FAC and the quantised instantaneous correlation provide a suitable basis with which to perform sound localisation tasks, a linear regression, an extreme learning machine, and a convolutional neural network are trained to learn the azimuthal angle of the sound source from the correlogram. The system is evaluated using speech data recorded in a reverberant environment. We compare the performance of the linear CAR and nonlinear CAR-FAC models with current sound localisation systems as well as with human performance.