We have processed 2774 high galactic observations from the XMM archive (as of 2010 May) and extracted a serendipitous catalogue of some 850 clusters of galaxies based on purely X-ray criteria, following the methodology developed for the XMM-Large-Scale Survey. Restricting the sample to the highest signal-to-noise ratio objects (347 clusters), we perform a cosmological analysis using only the X-ray information. The analysis consists in the modelling of the observed colour-magnitude count rate and hardness ratio (CR-HR) diagram constructed from cluster instrumental count rates measured in the 0.5-2, 1-2 and 0.5-1 keV bands. A Monte Carlo Markov chain procedure simultaneously fits the cosmological parameters, the evolution of the cluster scaling laws and the selection effects. Our results are consistent with the σ8 and Ωm values obtained by the 5-year Wilkinson Microwave Anisotropy Probe (WMAP5) and point towards a negative evolution of the cluster scaling relations with respect to the self-similar expectation. We are further able to constrain the cluster fractional radius x c,0=r c/R 500c to x c, 0= 0.24 ± 0.04. This study stresses again the critical role of selection effects in deriving cluster scaling relations, even in the local universe. Finally, we show that the CR-HR method applied to the eRosita all-sky survey - provided that cluster photometric redshifts are available - will enable the determination of the equation of state of the dark energy at the level of the Dark Energy Task Force (DETF) stage IV predictions; simultaneously, the evolution of the cluster scaling relations will be unambiguously determined. The XMM CLuster Archive Super Survey (X-CLASS) serendipitous cluster catalogue is available online at http://xmm-lss.in2p3.fr:8080/l4sdb/.