We present a new derivation of the CORS Baade–Wesselink method in the Walraven photometric system. We solved the complete Baade–Wesselink equation by calibrating the surface brightness function with a recent grid of atmosphere models. The new approach was adopted to estimate the mean radii of a sample of Galactic Cepheids for which are available precise light curves in the Walraven bands. Current radii agree, within the errors, quite well with Cepheid radii based on recent optical and near-infrared interferometric measurements. We also tested the impact of the projection factor on the period–radius relation using two different values (p= 1.36, 1.27) that bracket the estimates available in the literature. We found that the agreement of our period–radius relation with similar empirical and theoretical period–radius relations in the recent literature improves by changing the projection factor from p= 1.36 to 1.27. Our period–radius relation is log R= (0.75 ± 0.03)log P+ (1.10 ± 0.03), with an rms = 0.03 dex. Thanks to accurate estimates of the effective temperature of the selected Cepheids, we also derived the period–luminosity relation in the V band and we found MV= (−2.78 ± 0.11)log P+ (−1.42 ± 0.11) with rms = 0.13 mag, for p= 1.27. It agrees quite well with recent results in the literature, while the relation for p= 1.36 deviates by more than 2σ. We conclude that, even taking into account the intrinsic dispersion of the obtained period–luminosity relations that is roughly of the same order of magnitude as the effect of the projection factor, the results of this paper seem to favour the value p= 1.27.