The inclusive top quark pair ($t\bar{t}$) production cross-section $\sigma _{t\bar{t}}$ has been measured in proton–proton collisions at $\sqrt{s}=13\,\text {TeV}$, using 36.1 fb$^{-1}$ of data collected in 2015–2016 by the ATLAS experiment at the LHC. Using events with an opposite-charge $e\mu $ pair and b-tagged jets, the cross-section is measured to be: $\begin{aligned} \sigma _{t\bar{t}} = 826.4 \pm 3.6\,\mathrm {(stat)}\ \pm 11.5\,\mathrm {(syst)}\ \pm 15.7\,\mathrm {(lumi)}\ \pm 1.9\,\mathrm {(beam)}\,\mathrm {pb}, \end{aligned}$where the uncertainties reflect the limited size of the data sample, experimental and theoretical systematic effects, the integrated luminosity, and the LHC beam energy, giving a total uncertainty of 2.4%. The result is consistent with theoretical QCD calculations at next-to-next-to-leading order. It is used to determine the top quark pole mass via the dependence of the predicted cross-section on $m_t^{\mathrm{pole}}$, giving $m_t^{\mathrm{pole}}=173.1^{+2.0}_{-2.1}\,\text {GeV}$. It is also combined with measurements at $\sqrt{s}=7\,\text {TeV}$ and $\sqrt{s}=8\,\text {TeV}$ to derive ratios and double ratios of $t\bar{t}$ and Z cross-sections at different energies. The same event sample is used to measure absolute and normalised differential cross-sections as functions of single-lepton and dilepton kinematic variables, and the results are compared with predictions from various Monte Carlo event generators.