The Millennium Galaxy Catalogue (MGC) is a 37.5 deg2, medium-deep, B-band imaging survey along the celestial equator, taken with the Wide Field Camera on the Isaac Newton Telescope. The survey region is contained within the regions of both the Two Degree Field Galaxy Redshift Survey (2dFGRS) and the Sloan Digital Sky Survey Early Data Release (SDSS-EDR). The survey has a uniform isophotal detection limit of 26 mag arcsec-2 and it provides a robust, well-defined catalogue of stars and galaxies in the range 16 ≤ BMGC < 24 mag. Here we describe the survey strategy, the photometric and astrometric calibration, source detection and analysis, and present the galaxy number counts that connect the bright and faint galaxy populations within a single survey. We argue that these counts represent the state of the art and use them to constrain the normalizations (φ*) of a number of recent estimates of the local galaxy luminosity function. We find that the 2dFGRS, SDSS Commissioning Data (CD), ESO Slice Project, Century Survey, Durham/UKST, Mt Stromlo/APM, SSRS2 and NOG luminosity functions require a revision of their published φ* values by factors of 1.05 ± 0.05, 0.76 ± 0.10, 1.02 ± 0.22, 1.02 ± 0.16, 1.16 ± 0.28, 1.75 ± 0.37, 1.40 ± 0.26 and 1.01 ± 0.39, respectively. After renormalizing the galaxy luminosity functions we find a mean local h luminosity density jbJ̄ = (1.986 ± 0.031) × 108 h L⊙ Mpc-3 1.