Various forms of carbon nanotubes have been utilized in water treatment applications. The unique characteristics of carbon nanotubes, however, have not been fully exploited for such applications. Here we exploit the characteristics and corresponding attributes of carbon nanotubes to develop a millimetre-thick ultrafiltration membrane that can provide a water permeability that approaches 30,000 l m⁻² h⁻¹ bar⁻¹, compared with the best water permeability of 2,400 l m⁻² h⁻¹ bar⁻¹ reported for carbon nanotube membranes. The developed membrane consists only of vertically aligned carbon nanotube walls that provide 6-nm-wide inner pores and 7-nm-wide outer pores that form between the walls of the carbon nanotubes when the carbon nanotube forest is densified. The experimental results reveal that the permeance increases as the pore size decreases. The carbon nanotube walls of the membrane are observed to impede bacterial adhesion and resist biofilm formation.