This dataset contains postprocessed numerical data from direct numerical simulations performed using the CgLES code of turbulent flow over a regular array of rectangular 2Hx1Hx1H buildings for two different wind directions: domain size 12Hx9Hx8H for 0 degrees and 12Hx12Hx12H for 45 degrees. The data contain horizontally-averaged profiles, as well as vertical and horizontal profiles at specific locations, of selected first and second-order turbulent flow statistics. Further computational details are given in the article 'Measurements and computations of flow in an urban street system' by Castro et al., Boundary-Layer Meteorol. 162, 207-230 (2017). CgLES is a parallel code for performing large-eddy simulations (LES) and direct numerical simulations (DNS) over complex geometry, developed at the University of Southampton. Details of the numerical methods are given in the article Coceal et al., J. Fluid Mech. 589, 375-409.