The LHCb Collaboration is constructing a large scintillating fibre tracker for a major upgrade of the experiment during the LHC long shutdown LS2 scheduled for 2019-2020. The detector is based on blue emitting Kuraray SCSF-78MJ fibres of 0.25 mm diameter, read out by linear 128-channel Hamamatsu SiPM arrays. Over a period of about 2 years the full supply of 12,000 km of fibres underwent a systematic and rigorous quality assurance program, including geometrical refinement to deal with rare punctual imperfections. The measurements comprised attenuation length, ionisation light yield, diameter, cladding integrity and radiation tolerance to X-rays. The supply was found to be timely and of very high quality and stability, which led to negligible rejection rates. A small but systematic degradation of the attenuation length by about 1.4% per year is interpreted as natural aging due to oxidation of the polystyrene fibre core and is subject of further investigations.