Here we describe using nanosheets of both graphene and boron nitride, produced by liquid phase exfoliation, as fillers in composite fibres. The fibres were prepared by coagulation spinning using polyvinylalcohol as a matrix. We obtained good quality fibres with diameter and nanosheet volume fraction which could be controlled via the ratio of nanosheet to polymer injection rates. The mechanical stiffness (modulus, Y) and strength, σB, increased relatively slowly with volume fraction (dY/dVf 160 GPa and dσB/dVf 0.8 GPa). However, both stiffness and strength continued increasing with nanosheet content to loading levels of ~20vol%, after which the properties fell off. Such relatively high loading levels result in impressive mechanical properties with stiffness and strength of up to 30 GPa and 260 MPa observed. In addition, we found the graphene-filled fibres to be electrically conducting with conductivities of up to 3 S/m.