We present the measurements of the differential cross-sections for inclusive electron and muon production in proton–proton collisions at a centre-of-mass energy of s√= 7 TeV, using ∼1.4 pb − 1 of data collected by the ATLAS detector at the Large Hadron Collider. The muon cross-section is measured as a function of muon transverse momentum p T in the range 4 < p T < 100 GeV and within pseudorapidity |η| < 2.5. In addition, the electron and muon cross-sections are measured in the range 7 < p T < 26 GeV and within |η| < 2.0, excluding 1.37 < |η| < 1.52. 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-p T resummation, and to be sensitive to the effects of NLL resummation.