  The amplitude of density perturbations, for the currently-favoured LambdaCDM
cosmology, is constrained using the observed properties of galaxy clusters. The
catalogue used is that of Ikebe et al. (2002). The cluster temperature to mass
relation is obtained via N-body/hydrodynamical simulations including radiative
cooling and preheating of cluster gas, which we have previously shown to
reproduce well the observed temperature--mass relation in the innermost parts
of clusters (Thomas et al. 2002). We generate and compare mock catalogues via a
Monte Carlo method, which allows us to constrain the relation between X-ray
temperature and luminosity, including its scatter, simultaneously with
cosmological parameters. We find a luminosity-temperature relation in good
agreement with the results of Ikebe et al. (2002), while for the matter power
spectrum normalization, we find $\sigma_8 = 0.78_{-0.06}^{+0.30}$ at 95 per
cent confidence for $\Omega_0 = 0.35$. Scaling to WMAP's central value of
$\Omega_0 = 0.27$ would give a best-fit value of $\sigma_8 \simeq 0.9$.
