The differential cross section for the process Z/γ * → ℓℓ (ℓ = e, μ) as a function of dilepton invariant mass is measured in pp collisions at √s = 7 TeV at the LHC using the ATLAS detector. The measurement is performed in the e and μ channels for invariant masses between 26 GeV and 66 GeV using an integrated luminosity of 1.6 fb -1 collected in 2011 and these measurements are combined. The analysis is extended to invariant masses as low as 12 GeV in the muon channel using 35 pb-1 of data collected in 2010. The cross sections are determined within fiducial acceptance regions and corrections to extrapolate the measurements to the full kinematic range are provided. Next-to-next-to-leading- order QCD predictions provide a significantly better description of the results than next-to-leading-order QCD calculations, unless the latter are matched to a parton shower calculation