We present new measurements of the luminosity function (LF) of luminousred galaxies (LRGs) from the Sloan Digital Sky Survey (SDSS) and the 2dFSDSS LRG and Quasar (2SLAQ) survey. We have carefully quantified, andcorrected for, uncertainties in the K and evolutionary corrections,differences in the colour selection methods, and the effects ofphotometric errors, thus ensuring we are studying the same galaxypopulation in both surveys. Using a limited subset of 6326 SDSS LRGs(with 0.17 < z < 0.24) and 1725 2SLAQ LRGs (with 0.5 < z <0.6), for which the matching colour selection is most reliable, we findno evidence for any additional evolution in the LRG LF, over thisredshift range, beyond that expected from a simple passive evolutionmodel. This lack of additional evolution is quantified using thecomoving luminosity density of SDSS and 2SLAQ LRGs, brighter thanM0.2r - 5 log h0.7 = -22.5, which are2.51 +/- 0.03 × 10-7LsolarMpc-3and 2.44 +/- 0.15 ×10-7LsolarMpc-3, respectively (<10per cent uncertainty). We compare our LFs to the COMBO-17 data and findexcellent agreement over the same redshift range. Together, thesesurveys show no evidence for additional evolution (beyond passive) inthe LF of LRGs brighter than M0.2r - 5 logh0.7 = -21 (or brighter than ~L*). We test our SDSS and 2SLAQLFs against a simple `dry merger' model for the evolution of massive redgalaxies and find that at least half of the LRGs at z ~= 0.2 mustalready have been well assembled (with more than half their stellarmass) by z ~= 0.6. This limit is barely consistent with recent resultsfrom semi-analytical models of galaxy evolution.