This is the second in a series of papers in which we derive simultaneous constraints on cosmology and X-ray scaling relations using observations of massive, X-ray flux-selected galaxy clusters. The data set consists of 238 clusters with 0.1–2.4 keV luminosities >2.5 × 1044 h−270 erg s−1, and incorporates follow-up observations of 94 of those clusters using the Chandra X-ray Observatory or ROSAT (11 were observed with both). The clusters are drawn from three samples based on the ROSAT All-Sky Survey: the ROSAT Brightest Cluster Sample (78/37 clusters detected/followed-up), the ROSAT-ESO Flux-Limited X-ray sample (126/25) and the bright sub-sample of the Massive Cluster Survey (34/32). Our analysis accounts self-consistently for all selection effects, covariances and systematic uncertainties. Here we describe the reduction of the follow-up X-ray observations, present results on the cluster scaling relations, and discuss their implications. Our constraints on the luminosity–mass and temperature–mass relations, measured within r500, lead to three important results. First, the data support the conclusion that excess heating of the intracluster medium (or a combination of heating and condensation of the coldest gas) has altered its thermodynamic state from that expected in a simple, gravitationally dominated system; however, this excess heat is primarily limited to the central regions of clusters (r < 0.15r500). Secondly, the intrinsic scatter in the centre-excised luminosity–mass relation is remarkably small, being bounded at the <10 per cent level in current data; for the hot, massive clusters under investigation, this scatter is smaller than in either the temperature–mass or YX–mass relations (10–15 per cent). Thirdly, the evolution with redshift of the scaling relations is consistent with the predictions of simple, self-similar models of gravitational collapse, indicating that the mechanism responsible for heating the central regions of clusters was in operation before redshift 0.5 (the limit of our data) and that its effects on global cluster properties have not evolved strongly since then. Our results provide a new benchmark for comparison with numerical simulations of cluster formation and evolution.