We have prepared composite fibres based on the polyester, polyethylene terephthalate (PET), filled with both single walled nanotubes and graphene by a combination of solution and melt processing. On addition of ≤2 wt% filler we observe increases in both modulus and strength by factors of between ×2 and ×4 for both fillers. For the nanotube-based fibres, the mechanical properties depend strongly on fibre diameter due to a combination of defect and nanotube orientation effects. For the graphene filled fibres, the modulus is approximately invariant with diameter while the strength is defect limited, scaling weakly with diameter. Using this production method, the best fibre we prepared had modulus and strength of 42 GPa and 1.2 GPa respectively (2 wt% SWNT). We attribute this reinforcement predominately to the dispersion quality resulting from the solvent exfoliation of both nanotubes and graphene. In general, marginally better reinforcement was observed for the nanotube filled fibres. However, because of the low cost of graphite, we suggest graphene to be the superior reinforcement material for polymer fibres.