We present the analysis of a new flux-limited sample of bright quasars and Seyfert 1 galaxies in an effective area of 611 square deg, drawn from the Hamburg/ESO survey. We confirm recent claims that bright quasars have a higher surface density than previously thought. Special care was taken to avoid morphological and photometric biases against low-redshift quasars, and about 50 % of the sample objects are at z < 0.3, spanning a range of three decades in luminosity. While our derived space densities for low-luminosity Seyfert 1 nuclei are consistent with those found in the literature, we find that luminous QSOs, M_B < -24, are much more numerous in the local universe than previous surveys indicated. The optical luminosity functions of Seyfert 1 nuclei and QSOs join smoothly, and if the host galaxy contributions are taken into account, a single power-law of slope alpha = -2.2 describes the combined local luminosity function adequately, over the full range in absolute magnitude. Comparing our data with published results at higher redshifts, we can rule out pure luminosity evolution as an acceptable parametrisation; the luminosity function of quasars changes shape and slope with z, in the sense that the most luminous quasars show the weakest evolution.
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