The Gaia-ESO Public Spectroscopic Survey (GES) is conducting a large-scale study of multi-element chemical abundances of some 100 000 stars in the Milky Way with the ultimate aim of quantifying the formation history and evolution of young, mature and ancient Galactic populations. However, in preparing for the analysis of GES spectra, it has been noted that atomic oscillator strengths of important Fe I lines required to correctly model stellar line intensities are missing from the atomic data base. Here, we present new experimental oscillator strengths derived from branching fractions and level lifetimes, for 142 transitions of Fe I between 3526 and 10 864 Å, of which at least 38 are urgently needed by GES. We also assess the impact of these new data on solar spectral synthesis and demonstrate that for 36 lines that appear unblended in the Sun, Fe abundance measurements yield a small line-by-line scatter (0.08 dex) with a mean abundance of 7.44 dex in good agreement with recent publications.