The lifetimes of the first excited 2+ states in 62Fe and 64Fe have been measured in an experiment at GANIL using the Recoil-Distance Doppler Shift technique. The iron nuclei where populated in multi-nucleon transfer reactions between a 238U beam at 6.5MeV/A and a 64Ni target. A degrader foil at micrometer distances from the target was used to slow the reaction products before entering the VAMOS spectrometer for identification. The Doppler shift of the gamma rays emitted before and after the degrader foil was measured with the EXOGAM germanium detector array. The lifetimes give evidence for a strong increase in collectivity from 62Fe to 64Fe. The results are compared to new large-scale shell model calculations and HFB-based configuration mixing calculations. The large B(E2) value in 64Fe can be related to the occupation of the neutron g9/2 and d5/2 orbitals. Many parallels are found between the neutron-rich Fe isotopes below 68Ni and the so-called 'island if inversion' around 32Mg