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The spectroscopic quadrupole moments of the odd–even Mn isotopes between N=28 and N=38 have been measured using bunched-beam collinear laser spectroscopy at ISOLDE, CERN. In order to increase sensitivity to the quadrupole interaction, the measurements have been done using a transition in the ion rather than in the atom, with the additional advantage of better spectroscopic efficiency. Since the chosen transition is from a metastable state, optical pumping in ISOLDE's cooler and buncher (ISCOOL) was used to populate this state. The extracted quadrupole moments are compared to large-scale shell model predictions using three effective interactions, GXPF1A, LNPS and modified A3DA. The inclusion of both the 1νg9/2 and 2νd5/2 orbitals in the model space is shown to be necessary to reproduce the observed increase in the quadrupole deformation from N=36 onwards. Specifically, the inclusion of the 2νd5/2 orbital induces an increase in neutron and proton excitations across the reduced gaps at N=40 and Z=28, leading to an increase in deformation above N=36.