We present a new photometric catalogue of the rich globular cluster (GC) system around M87, the brightest cluster galaxy in Virgo. Using archival Next Generation Virgo Cluster Survey images in the ugriz bands, observed with Canada-France-Hawaii Telescope/MegaPrime, we perform a careful subtraction of the galaxy's halo light in order to detect objects at small galactocentric radii as well as in the wider field, and find 17620 GC candidates over a radius range from 1.3 to 445kpc with g<24mag. By inferring their colour, radial and magnitude distributions in a Bayesian way, we find that they are well described as a mixture of two GC populations and two distinct contaminant populations, but confirm earlier findings of radius-dependent colour gradients in both GC populations. This is consistent with a picture in which the more enriched GCs reside deeper in the galaxy's potential well, indicating a role for dissipative collapse in the formation of both the red and the blue GCs.