The inclusive top quark pair (tt ¯) cross-section σtt ¯ has been measured in proton–proton collisions at √s = 13 TeV, using 140 fb−1 of data collected by the ATLAS experiment at the Large Hadron Collider. Using events with an opposite-charge eμ pair and b-tagged jets, the crosssection is measured to be: σtt ¯ = 829.3 ± 1.3 (stat) ± 8.0 (syst) ± 7.3 (lumi) ±1.9 (beam) pb, where the uncertainties reflect the limited size of the data sample, experimental and theoretical systematic effects, the integrated luminosity, and the proton beam energy, giving a total uncertainty of 1.3%. The result is used to determine the top quark pole mass via the dependence of the predicted cross-section on mpole t , giving mpole t = 172.8+1.5 −1.7 GeV. The same event sample is used to measure absolute and normalised differential cross-sections for the tt ¯ → eμνν¯bb¯ process as a function of single-lepton and dilepton kinematic variables. Complementary measurements of eμbb¯ production, treating both tt ¯ and Wt events as signal, are also provided. Both sets of differential cross-sections are compared to the predictions of various Monte Carlo event generators, demonstrating that the state-of-the-art generators Powheg MiNNLO and Powheg bb4l describe the data better than Powheg hvq.