Measurements of W$^{+}$W$^{−}$ → e$^{±}$νμ$^{∓}$ν production cross-sections are presented, providing a test of the predictions of perturbative quantum chromodynamics and the electroweak theory. The measurements are based on data from pp collisions at $ \sqrt{s} $ = 13 TeV recorded by the ATLAS detector at the Large Hadron Collider in 2015–2018, corresponding to an integrated luminosity of 140 fb$^{−1}$. The number of events due to top-quark pair production, the largest background, is reduced by rejecting events containing jets with b-hadron decays. An improved methodology for estimating the remaining top-quark background enables a precise measurement of W$^{+}$W$^{−}$ cross-sections with no additional requirements on jets. The fiducial W$^{+}$W$^{−}$ cross-section is determined in a maximum-likelihood fit with an uncertainty of 3.1%. The measurement is extrapolated to the full phase space, resulting in a total W$^{+}$W$^{−}$ cross-section of 127 ± 4 pb. Differential cross-sections are measured as a function of twelve observables that comprehensively describe the kinematics of W$^{+}$W$^{−}$ events. The measurements are compared with state-of-the-art theory calculations and excellent agreement with predictions is observed. A charge asymmetry in the lepton rapidity is observed as a function of the dilepton invariant mass, in agreement with the Standard Model expectation. A CP-odd observable is measured to be consistent with no CP violation. Limits on Standard Model effective field theory Wilson coefficients in the Warsaw basis are obtained from the differential cross-sections.[graphic not available: see fulltext]