A thorough study of the generation of modulation instability (MI) in distributed Brillouin fibre sensors is presented. ASE noise co-propagating with the pump pulses within the MI gain spectrum has been identified to be an important factor seeding modulation instability and reducing its power threshold. The paper describes how optical narrowband filtering reduces the pump depletion resulting from MI, allowing pump pulses to propagate through longer distances in standard optical single-mode fibres.