The invention provides a method for the purification of a liquid by membrane distillation comprising: - passing a heated vapourising stream of a liquid (retentate stream) through a retentate channel over a porous membrane, whereby vapour of the liquid flows via the pores of the membrane to the other side of said membrane, and - condensing said vapour on the other side of said membrane to give a distillate stream in a distillate channel which distillate is created by passing the heat of condensation (latent heat) towards a condenser surface, said condenser surface forming a non-porous separation between a feed stream of the liquid to be purified and said distillate stream, which feed stream is passed through a feed channel in counter-current with the retentate stream, whereby at least part of the latent heat is transferred via the condenser surface to the feed stream, characterised in that, a positive liquid pressure difference is applied between the retentate stream and the feed stream at the corresponding points of the retentate channel and the feed channel over at least a part of each of the retentate channel and feed channel. The invention further provides an apparatus suitable for use in said method.