To assess the effect of baryonic 'pinching' of galaxy cluster dark matter (DM) haloes, cosmological (A cold dark matter) TREESPH simulations of the formation and evolution of two galaxy clusters have been performed, with and without baryons included. The simulations with baryons invoke star formation, chemical evolution with non-instantaneous recycling, metallicity-dependent radiative cooling, strong starburst-driven galactic superwinds and the effects of a meta-galactic ultraviolet field, including simplified radiative transfer. The two clusters have T similar or equal to 3 and 6 keV, respectively, and, at z similar to 0, both host a prominent, central cD galaxy. Comparing the simulations without and with baryons, it is found for the latter that the inner DM density profiles, r less than or similar to 50-100 kpc, steepen considerably: Delta alpha similar to 0.5-0.6, where -alpha is the logarithmic DM density gradient. This is primarily due to the central stellar cDs becoming very massive, as a consequence of the onset of late-time cooling flows and related star formation. Once these spurious cooling flows have been corrected for, and the cluster gravitational potentials dynamically adjusted, much smaller pinching effects are found: Delta alpha similar to 0.1. Including the effects of baryonic pinching, central slopes of alpha similar or equal to 1.0 and 1.2 are found for the DM in the two clusters, interestingly close to recent observational findings for galaxy cluster Abell 1703 based on strong gravitational lensing. For the simulations with baryons, the inner density profile of DM and cluster gas (intracluster medium) combined is found to be only very marginally steeper than that of the DM, Delta alpha less than or similar to 0.05. However, the total matter inner density profiles are found to be Delta alpha similar to 0.5 steeper than the inner profiles in the DM-only simulations.