We have developed a picosecond-timescale all-optical switch which operates at the single photon level. The switch is based on the Kerr effect in just 10cm of commercial single-mode fibre. A strong ultrafast pump pulse induces polarization rotation of single photons with near-unit efficiency. Careful choice of the pump pulse energy, length of the fibre, and the relevant group velocities limit the noise floor of the switch to around 10-4 photons per pump pulse. In this talk I will outline the development of the switch, and discuss its application in optical signal processing and quantum information science.