Retinal ganglion cells, the sole output neurons of the retina, exhibit surprising diversity. A recent study reported over 30 distinct types in the mouse retina, indicating that the processing of visual information is highly parallelised in the brain. The advent of high density multi-electrode arrays now enables recording from many hundreds to thousands of neurons from a single retina. Here we describe a method for the automatic classification of large-scale retinal recordings using a simple stimulus paradigm and a spike train distance measure as a clustering metric. We evaluate our approach using synthetic spike trains, and demonstrate that major known cell types are identified in high-density recording sessions from the mouse retina with around 1,000 retinal ganglion cells. A comparison across different retinas reveals substantial variability between preparations, suggesting pooling data across retinas should be approached with caution. As a parameter-free method, our approach is broadly applicable for cellular physiological classification in all sensory modalities.