In their original formulation of superconductivity, the London brothers predicted1 the exponential suppression of an electrostatic field inside a superconductor over the so-called London penetration depth2-4, λL. Despite a few experiments indicating hints of perturbation induced by electrostatic fields5-7, no clue has been provided so far on the possibility to manipulate metallic superconductors via the field effect. Here, we report field-effect control of the supercurrent in all-metallic transistors made of different Bardeen-Cooper-Schrieffer superconducting thin films. At low temperature, our field-effect transistors show a monotonic decay of the critical current under increasing electrostatic field up to total quenching for gate voltage values as large as ±40 V in titanium-based devices. This bipolar field effect persists up to ~85% of the critical temperature (~0.41 K), and in the presence of sizable magnetic fields. A similar behaviour is observed in aluminium thin-film field-effect transistors. A phenomenological theory accounts for our observations, and points towards the interpretation in terms of an electric-field-induced perturbation propagating inside the superconducting film. In our understanding, this affects the pairing potential and quenches the supercurrent. These results could represent a groundbreaking asset for the realization of all-metallic superconducting field-effect electronics and leading-edge quantum information architectures8,9.