We suggest that narrow, long radio filaments near the Galactic Centre arise as kinetic jets - streams of high-energy particles escaping from ram pressure confined pulsar wind nebulae (PWNe). The reconnection between the PWN and interstellar magnetic field allows pulsar wind particles to escape, creating long narrow features. They are the low-frequency analogues of kinetic jets seen around some fast-moving pulsars, such as The Guitar and The Lighthouse PWNe. The radio filaments trace a population of pulsars also responsible for the Fermi GeV excess produced by the Inverse Compton scattering by the pulsar wind particles. The magnetic flux tubes are stretched radially by the large-scale Galactic winds. In addition to PWNe accelerated particles can be injected at supernovae remnants. The model predicts variations of the structure of the largest filaments on scales of ∼dozens of years - smaller variations can occur on shorter time-scales. We also encourage targeted observations of the brightest sections of the filaments and of the related unresolved point sources in search of the powering PWNe and pulsars.