For turbulent flows in porous media, it is often assumed that the irregularity of the matrix would not affect the macroscopic, double‐averaged (in time and space), parameters of turbulence. Hence, to improve currently used modelling techniques, the ongoing efforts of the community are focused on performing high‐fidelity, scale‐resolving simulations of flows in regular, periodically repeating porous structures. This approach allows for minimizing still large computational cost, however, it assumes that results obtained from those geometries are generalizable to more disordered configurations. We investigate this assumption numerically using large‐eddy simulation and analyse the influence of the irregularity of the porous structure on turbulent characteristics in a fully turbulent flow in a channel half‐filled with porous medium. The flow statistics are examined and compared between four simulations, a reference channel with regular three‐dimensional porous matrix consisting of an array of cubes and three similar geometries created from randomly perturbing the positions of the cubes, with increasing mean value of cube displacement. We study double‐averaged flow properties, the distributions of double‐averaged Reynolds stress tensor, including the anisotropy of macroscopic turbulence and the drag force induced by the flow in the porous region of the channel. The results confirm the idea that the averaged characteristics, including the anisotropy of the stress tensor and the drag force, are not greatly influenced by the moderate perturbation to the geometry of the porous matrix. Additionally, the macroscopic turbulence seems to exhibit a high degree of anisotropy in the porous region and the adjacent boundary layer, suggesting that second‐order closure could be an adequate modelling choice for such flows. [ABSTRACT FROM AUTHOR]