The composition comprises a mixture of: i) poly(L-, D-lactide) homopolymer and, optionally, poly(ε-caprolactone) homopolymer, and ii) poly(L-lactide) and poly(ε-caprolactone) diblock copolymer, where said copolymer has a molar mass of the L-lactide block of 20,000 g/mol to 200,000 g/mol and a molar mass of the ε-caprolactone block of 10,000 g/mol to 100,000 g/mol, with the molar ratio between the L-lactide block and the ε-caprolactone block of 2:1. The invention also refers to the nanostructured material obtained from this composition that is characterised by a nanostructure of two mutually self-assembled phases, one phase being formed by a polymeric matrix of poly(L-, D-lactide) units and the other phase by poly(ε-caprolactone) units self-assembled with the matrix and also its use for the manufacture of a plastic article in the form of a transparent film or thin sheet.