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 along a porous hydrophobic membrane (10), 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 (5) which distillate is created by passing the heat of condensation (latent heat) towards a condenser surface (3), 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 (2) in counter-current with the retentate stream, in which feed channel a space material (4) is arranged whereby at least part of the latent heat is transferred via the condenser surface to the feed stream, and whereby 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 (9) and feed channel. The invention further provides an apparatus suitable for use in said method.