A carbon nanotube free-standing linearly dichroic polariser is developed using solid-state extrusion. Membrane cohesion is experimentally and numerically demonstrated to derive from inter-tube van der Waals interactions in this family of planar metastable morphologies, controlled by the chemical vapour deposition conditions. Ultra-broadband polarisation (400 nm – 2.5 mm) is shown and corroborated by effective medium and full numerical simulations.