We have investigated the double ionization of helium induced by 45 fs, 394 nm linearly polarized laser pulses for intensities (2.5–150) × 1014 W cm−2. The time evolution of the process was determined by applying the classical ensemble approximation (CEA) model. The results of the calculations obtained for the double-to-single ionization ratio, the momentum distribution of the He2+ recoil ion and the correlated two-electron momentum distribution are compared with the recent experimental data of Henrichs et al (2018 Phys. Rev. A 98 043405). The standard CEA model failed to reproduce the basic features of the experiment. A considerable improvement in the description of the experimental data was achieved by including a two-step process in the model: the formation of a transient double excited state in the first step, and the simultaneous release of the two electrons via ‘over the barrier ionization’ in the second step.