Travelling-wave solutions are shown to bifurcate from relative periodic orbits in plane Poiseuille flow at   in a saddle-node infinite-period bifurcation. These solutions consist in self-sustaining sinuous quasi-streamwise streaks and quasi-streamwise vortices located in the bulk of the flow. The lower branch travelling-wave solutions evolve into spanwise localized states when the spanwise size   of the domain in which they are computed is increased. On the contrary, the upper branch of travelling-wave solutions develops multiple streaks when   is increased. Upper-branch travelling-wave solutions can be continued into coherent solutions to the filtered equations used in large-eddy simulations where they represent turbulent coherent large-scale motions.