A measurement of angular correlations in Drell–Yan lepton pairs via the ϕη* observable is presented. This variable probes the same physics as the Z/γ* boson transverse momentum with a better experimental resolution. The Z/γ*→e+e−Z/γ⁎→e+e− and Z/γ⁎→μ+μ−Z/γ*→μ+μ− decays produced in proton–proton collisions at a centre-of-mass energy of √s=7 TeV are used. The data were collected with the ATLAS detector at the LHC and correspond to an integrated luminosity of 4.6 fb−1. Normalised differential cross sections as a function of ϕη* are measured separately for electron and muon decay channels. These channels are then combined for improved accuracy. The cross section is also measured double differentially as a function of ϕη* for three independent bins of the Z boson rapidity. The results are compared to QCD calculations and to predictions from different Monte Carlo event generators. The data are reasonably well described, in all measured Z boson rapidity regions, by resummed QCD predictions combined with fixed-order perturbative QCD calculations or by some Monte Carlo event generators. The measurement precision is typically better by one order of magnitude than present theoretical uncertainties.