A measurement of angular correlations in Drell-Yan lepton pairs via the $\phi^*$ observable is presented. This variable probes the same physics as the $Z/\gamma^*$ boson transverse momentum with a better experimental resolution. The $Z/\gamma^* \to ee$ and $Z/\gamma^* \to \mu \mu$ decays produced in proton--proton collisions at a centre-of-mass energy of $\sqrt{s} = 7 \text{TeV}$ are used. Normalised differential cross sections as a function of $\phi^*$ are measured separately for electron and muon decay channels. The cross-section is also measured double differentially as a function of $\phi^*$ for three independent bins of the $Z$ boson rapidity.