Conducting fibres are essential to the development of e-textiles. We demonstrate a method to make common insulating textile fibres conductive, by coating them with graphene. The resulting fibres display sheet resistance values as low as 600 Ωsq-1, demonstrating that the high conductivity of graphene is not lost when transferred to textile fibres. An extensive microscopic study of the surface of graphene-coated fibres is presented. We show that this method can be employed to textile fibres of different materials, sizes and shapes, and to different types of graphene. These graphene-based conductive fibres can be used as a platform to build integrated electronic devices directly in textiles.