This Letter presents measurements of the differential cross-sections for inclusive electron and muon production in proton–proton collisions at a centre-of-mass energy of , using data collected by the ATLAS detector at the LHC. The muon cross-section is measured as a function of pT in the range 4<pT<100 GeV and within pseudorapidity |η|<2.5. In addition the electron and muon cross-sections are measured in the range 7<pT<26 GeV and within |η|<2.0, excluding 1.37<|η|<1.52. Integrated luminosities of 1.3 pb−1 and 1.4 pb−1 are used for the electron and muon measurements, respectively. After subtraction of the W/Z/γ^⁎ contribution, the differential cross-sections are found to be in good agreement with theoretical predictions for heavy-flavour production obtained from Fixed Order NLO calculations with NLL high-pT resummation, and to be sensitive to the effects of NLL resummation.