ABSTRACT We present cross-sections and rate coefficients for rotational transitions in the water isotopologues D2O, H$_2^{18}$O, and HDO induced by collisions with para-H2(j2 = 0) and ortho-H2(j2 = 1). Quantum scattering calculations are performed at the full close-coupling level with the isotopic variants of an accurate full-dimensional H2O−H2 interaction potential. The D2O, H$_2^{18}$O, and HDO cross-sections are compared to the corresponding cross-sections for H2O. Large isotopic effects are observed in the case of D2O and HDO, in particular for collisions with p-H2(j2 = 0), while the 18O isotopic substitution is found to be negligible. Rate coefficients are provided for rotational transitions among all para-D2O, ortho-D2O, and HDO levels with internal energy below 300 cm−1 and for kinetic temperatures in the range 5–300 K. Non-LTE radiative transfer calculations show that the HDO 225.9 GHz and H$_2^{18}$O 203.4 GHz transitions recently detected with ALMA in the young proto-planetary disc V883 Ori should be inverted (weak masers) in a large fraction of the disc.