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 root s = 7 TeV, using data collected by the ATLAS detector at the LHC. The muon cross-section is measured as a function of p(T) in the range 4 < p(T) < 100 GeV and within pseudorapidity vertical bar eta vertical bar < 2.5. In addition the electron and muon cross-sections are measured in the range 7 < p(T) < 26 GeV and within vertical bar eta vertical bar < 2.0, excluding 1.37 < vertical bar eta vertical bar < 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/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(T) resummation, and to be sensitive to the effects of NLL resummation. (C) 2011 CERN. Published by Elsevier B.V. All rights reserved.