The scaling of active photonic devices to deep-submicron length scales has been hampered by the fundamental diffraction limit and the absence of materials with sufficiently strong electro-optic effects. Plasmonics is providing new opportunities to circumvent this challenge. Here we provide evidence for a solid-state electro-optical switching mechanism that can operate in the visible spectral range with an active volume of less than (5 nm)(3) or ∼10(-6) λ(3), comparable to the size of the smallest electronic components. The switching mechanism relies on electrochemically displacing metal atoms inside the nanometre-scale gap to electrically connect two crossed metallic wires forming a cross-point junction. These junctions afford extreme light concentration and display singular optical behaviour upon formation of a conductive channel. The active tuning of plasmonic antennas attached to such junctions is analysed using a combination of electrical and optical measurements as well as electron energy loss spectroscopy in a scanning transmission electron microscope.