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 $\sqrt{s} = 7$ 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 $p_{\text{T}}$ in the range $4 < p_{\text{T}} < 100$ GeV and within pseudorapidity $|\eta| < 2.5$. In addition, the electron and muon cross-sections are measured in the range $7 < p_{\text{T}} < 26$ GeV and within $|\eta| < 2.0$, excluding $1.37 < |\eta| < 1.52$. After subtraction of the$ W/Z/\gamma^{*}$ 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-$p_{\text{T}}$ resummation, and to be sensitive to the effects of NLL resummation.