The inclusive top quark pair (tt) production cross-section σtt has been measured in proton–proton collisions at √s = 7 TeV and√s = 8 TeV with the ATLAS experiment at the LHC, using tt events with an opposite-charge eμ pair in the final state. The measurement was performed with the 2011 7 TeV dataset corresponding to an integrated luminosity of 4.6 fb−1 and the 2012 8 TeV dataset of 20.3 fb−1. The numbers of events with exactly one and exactly two b-tagged jets were counted and used to simultaneously determine σtt and the efficiency to reconstruct and b-tag a jet from a top quark decay, thereby minimising the associated systematic uncertainties. The cross-section was measured to be: σtt = 182.9 ± 3.1 ± 4.2 ± 3.6 ± 3.3 pb (√s = 7 TeV) and σtt = 242.4 ± 1.7 ± 5.5 ± 7.5 ± 4.2 pb (√s = 8 TeV), where the four uncertainties arise from data statistics, experimental and theoretical systematic effects, knowledge of the integrated luminosity and of the LHC beam energy. The results are consistent with recent theoretical QCD calculations at next-to-next-to-leading order. Fiducial measurements corresponding to the experimental acceptance of the leptons are also reported, together with the ratio of cross-sections measured at the two centre-of-mass energies. The inclusive cross-section results were used to determine the top quark pole mass via the dependence of the theoretically predicted cross-section on mpolet giving a result of mpolet = 172.9+2.5−2.6 GeV. By looking for an excess of tt production with respect to the QCD prediction, the results were also used to place limits on the pair-production of supersymmetric top squarks t1 with masses close to the top quark mass, decaying via t1 → t χ01 to predominantly right-handed top quarks and a light neutralino χ01, the lightest supersymmet-ric particle. Top squarks with masses between the top quark mass and 177 GeV are excluded at the 95 % confidence level.