  We recover the joint and individual space density and surface brightness
distribution(s) of galaxies from the Millennium Galaxy Catalogue. The MGC is a
local survey spanning 30.9 sq deg and probing approximately one--two mag/sq
arcsec deeper than either the Two-Degree Field Galaxy Redshift Survey (2dFGRS)
or the Sloan Digital Sky Survey (SDSS). The MGC contains 10,095 galaxies to
B_mgc < 20 mag with 96 per cent spectroscopic completeness. We implement a
joint luminosity-surface brightness step-wise maximum likelihood method to
recover the bivariate brightness distribution (BBD) inclusive of most selection
effects. Integrating the BBD over surface brightness we recover the following
Schechter function parameters: phi* = (0.0177 +/- 0.0015) h^3 Mpc^{-3}, M_{B}*
- 5 log h = (-19.60 +/- 0.04) mag and alpha =-1.13 +/- 0.02. Compared to the
2dFGRS (Norberg et al 2002) we find a consistent M* value but a slightly
flatter faint-end slope and a higher normalisation, resulting in a final
luminosity density j_{b_J} = (1.99 +/- 0.17) x 10^8 h L_{odot} Mpc^{-3}. The
MGC surface brightness distribution is a well bounded Gaussian at the M* point
with phi* = (3.5 +/- 0.1) x 10^{-2} h^3 Mpc^{-3}, mu^{e*} = (21.90 +/- 0.01)
mag/sq arcsec and sigma_{ln R_e} = 0.35 +/- 0.01. The characteristic surface
brightness for luminous systems is invariant to M_{B} - 5 log h ~ -19 mag
faintwards of which it moves to lower surface brightness. Higher resolution
(FWHM < 1 arcsec) and deeper (mu_eff > 26 mag/sq arcsec in the B-band)
observations of the local universe are now essential to probe to lower
luminosity and lower surface brightness levels. [abridged]
