The inclusive top quark pair ($$t\overline{t}$$) production cross-section $${\sigma _{t\overline{t}}}$$ has been measured in proton–proton collisions at $${\sqrt{s}=7~\mathrm{TeV}}$$ and $${\sqrt{s}=8~\mathrm{TeV}}$$ with the ATLAS experiment at the LHC, using $$t\overline{t}$$ events with an opposite-charge $$e\mu $$ pair in the final state. The measurement was performed with the 2011 7 TeV dataset corresponding to an integrated luminosity of 4.6 $${\mathrm{fb}^{-1}}$$ and the 2012 8 TeV dataset of 20.3 $${\mathrm{fb}^{-1}}$$. The numbers of events with exactly one and exactly two $$b$$-tagged jets were counted and used to simultaneously determine $${\sigma _{t\overline{t}}}$$ and the efficiency to reconstruct and $$b$$-tag a jet from a to...