In 1966, Pierre-Gilles de Gennes proposed a non-volatile mechanism for switching superconductivity on and off in a magnetic device. This involved a superconductor (S) sandwiched between ferromagnetic (F) insulators in which the net magnetic exchange field could be controlled through the magnetisation-orientation of the F layers. Because superconducting switches are attractive for a range of applications, extensive studies have been carried out on F/S/F structures. Although these have demonstrated a sensitivity of the superconducting critical temperature (T_c) to parallel (P) and antiparallel (AP) magnetisation-orientations of the F layers, corresponding shifts in T_c (i.e. ΔT_c = T_c,AP− T_c,P) are lower than predicted with ΔT_c only a small fraction of T_c,AP, precluding the development of applications. Here, we report EuS/Au/Nb/EuS structures where EuS is an insulating ferromagnet, Nb is a superconductor and Au is a heavy metal. For P magnetisations, the superconducting state in this structure is quenched down to the lowest measured temperature of 20 mK meaning that ΔT_c/T_c,AP is practically 1. The key to this so-called 'absolute switching' effect is a sizable spin-mixing conductance at the EuS/Au interface which ensures a robust magnetic proximity effect, unlocking the potential of F/S/F switches for low power electronics.