The transition rates for the 2(1)+ states in (62,64,66)Fe were studied using the recoil distance Doppler-shift technique applied to projectile Coulomb excitation reactions. The deduced E2 strengths illustrate the enhanced collectivity of the neutron-rich Fe isotopes up to N = 40. The results are interpreted using the generalized concept of valence proton symmetry which describes the evolution of nuclear structure around N = 40 as governed by the number of valence protons with respect to Z ≈ 30. The trend of collectivity suggested by the experimental data is described by state-of-the-art shell-model calculations with a new effective interaction developed for the fpgd valence space.