The large-scale structure in the distribution of galaxies is thought to arise from the gravitational instability of small fluctuations in the initial density field of the Universe. A key test of this hypothesis is that forming superclusters of galaxies should generate a systematic infall of other galaxies. This would be evident in the pattern of recessional velocities, causing an anisotropy in the inferred spatial clustering of galaxies. Here we report a precise measurement of this clustering, using the redshifts of more than 141,000 galaxies from the two-degree-field (2dF) galaxy redshift survey. We determine the parameter beta = Omega0.6/b = 0.43 +/- 0.07, where Omega is the total mass-density parameter of the Universe and b is a measure of the 'bias' of the luminous galaxies in the survey. (Bias is the difference between the clustering of visible galaxies and of the total mass, most of which is dark.) Combined with the anisotropy of the cosmic microwave background, our results favour a low-density Universe with Omega approximately 0.3.