We present a simple two-stage vapour-solid synthesis method for the growth of bismuth chalcogenide (Bi2Te3, Bi2Se3) topological insulator nanowires/nanobelts by using Bi2Se3 or Bi2Te3 powders as source materials. During the first stage of the synthesis process nanoplateteles, serving as "catalysts" for further nanowire/nanobelt growth, are formed. At a second stage of the synthesis, the introduction of a N2 flow at 35 Torr pressure in the chamber induces the formation of free standing nanowires/nanobelts. The synthesised nanostructures demonstrate a layered single-crystalline structure and Bi : Se and Bi : Te ratios 40 : 60 at% for both Bi2Se3 and Bi2Te3 nanowires/nanobelts. The presence of Shubnikov de Haas oscillations in the longitudinal magneto-resistance of the nanowires/nanobelts and their specific angular dependence confirms the existence of 2D topological surface states in the synthesised nanostructures.