The absence of any wide-separation gravitational lenses in the Large Bright Quasar Survey is used to place limits on the population of cluster-sized haloes in the universe, and hence constrain a number of cosmological parameters. The results agree with previous investigations in strongly ruling out the standard cold dark matter model but they are consistent with low-density universes in which the primordial fluctuation spectrum matches both cluster abundances and cosmic microwave background measurements. These conclusions are essentially independent of the cosmological constant, which is in stark contrast to the statistics of galaxy lenses. The constraints presented here are nullified if clusters have core radii of ≳10 kpc, but are free of a number of potential systematic errors, owing to the homogeneity of the data.