Timepix3 is a multi-purpose readout ASIC for hybrid pixel detectors. It can measure time and amplitude simultaneously by employing time-of-arrival (ToA) and time-over-threshold (ToT) techniques. Both methods are systematically affected by timewalk. In this paper, a method for pixel-by-pixel calibration of the time response is presented. Assemblies of Timepix3 ASICs bump-bonded to thin planar silicon pixel sensors with thicknesses of 50 μ m, 100 μ m and 150 μ m are calibrated and characterised in particle beams. For minimum ionising particles, time resolutions down to 0.72 ± 0.04 ns are achieved.