We report on the experimental realization and characterization of an asynchronous heralded single-photon source based on spontaneous parametric down-conversion. Photons at 1550 nm are heralded as being inside a single-mode fibre with more than 60% probability, and the multi-photon emission probability is reduced by a factor of up to more than 500 compared to Poissonian light sources. These figures of merit, together with the choice of telecom wavelength for the heralded photons, are compatible with practical applications needing very efficient and robust single-photon sources.