In the presence of macroscopic fibres of carbon nanotubes (CNT), various semicrystalline polymers are shown to present accelerated crystallisation through the formation of a transcrystalline (TC) layer perpendicular to the fibre axis. From differential scanning calorimetry, polarized optical microscopy and X-ray diffraction we establish this to be due to much faster nucleation rates at the fibre surface. The formation of a TC layers is demonstrated for polyvinyldene fluoride, isotactic polypropylene and poly(lactic acid) in spite of the large differences in their chemistry and structure unit cells, suggesting that epitaxy in terms of lattice type or size matching is not a prerequisite. For the three polymers as well as poly(ether ether ketone), the TC layer is identically oriented with the chain axis in the lamella parallel to the CNTs, as observed by wide and small angle X-ray scattering. These results point to polymer chain orientation at the point of adsorption and the formation of a mesomorphic layer as possible steps in the fast nucleation of oriented lamella, with wetting of the CNT fibre surface by the molten semi-crystalline polymer a key condition for heterogeneous nucleation to take place.