We present results from a study of the X-ray cluster population that forms within the CLEF cosmological hydrodynamics simulation, a large N-body/SPH simulation of the Lambda cold dark matter cosmology with radiative cooling, star formation and feedback. With nearly 100 (kT > 2 keV) clusters at z = 0 and 60 at z = 1, our sample is one of the largest ever drawn from a single simulation and allows us to study variations within the X-ray cluster population both at low and high redshift. The scaled projected temperature and entropy profiles at z = 0 are in good agreement with recent high-quality observations of cool core clusters, suggesting that the simulation grossly follows the processes that structure the intracluster medium (ICM) in these objects. Cool cores are a ubiquitous phenomenon in the simulation at low and high redshift, regardless of a cluster's dynamical state. This is at odds with the observations and so suggests there is still a heating mechanism missing from the simulation. The fraction of irregular (major merger) systems, based on an observable measure of substructure within X-ray surface brightness maps, increases with redshift, but always constitutes a minority population within the simulation. Using a simple, observable measure of the concentration of the ICM, which correlates with the apparent mass deposition rate in the cluster core, we find a large dispersion within regular clusters at low redshift, but this diminishes at higher redshift, where strong cooling-flow systems are absent in our simulation. Consequently, our results predict that the normalization and scatter of the luminosity-temperature relation should decrease with redshift; if such behaviour turns out to be a correct representation of X-ray cluster evolution, it will have significant consequences for the number of clusters found at high redshift in X-ray flux-limited surveys.