Surface pressure and wake velocity field fluctuations are investigated for a square cylinder mounted in the vicinity of a solid wall as functions of the boundary layer thickness and cylinder-to-wall gap heights for Reynolds number between 20000 and 40000. The study focuses on the suppression of vortex shedding occurring around critical gap heights. Mean data are combined to identify three distinct flow regimes. Time and frequency analyses show that at large gap heights periodic vortex shedding is perturbed by underlying large-scale structures leading to phase jitter and long-term loss of correlation. For small gaps, there is no evidence of periodic motion. For intermediate gap heights, there is a gradual loss of correlation between the pressure field on the top and lower cylinder surfaces, which leads to periods of sinusoidal fluctuations interspersed with incoherent motion in the wake. It is found that the Reynolds number influence is negligible and that an increase in the boundary layer thickness results in a reduction of the critical gap height. Stability considerations suggest that a stable vortex street can only exist for a certain range of the top shear layer to bottom shear layer circulation ratio.