We have exfoliated hexagonal boron nitride by ultrasonication in solutions of polyvinylalcohol in water. The resultant nanosheets are sterically stabilised by adsorbed polymer chains. Centrifugation-based size-selection was used to give dispersions of nanosheets with aspect ratio (length/thickness) of ∼1400. Such dispersions can be used to produce polyvinylalcohol–BN composite films. Helium ion microscopy of fracture surfaces shows the nanosheets to be well dispersed and the composites to fail by pull-out. We find both modulus, Y, and strength, σB, of these composites to increase linearly with volume fraction, Vf, up to Vf ∼ 0.1 vol% BN before falling off. The rates of increase are extremely high; dY/dVf = 670 GPa and dσB/dVf = 47 GPa. The former value matches theory based on continuum mechanics while the latter value is consistent with remarkably high polymer–filler interfacial strength. However, because the mechanical properties increase over such a narrow volume fraction range, the maximum values of both modulus and strength are only ∼40% higher than the pure polymer. This phenomenon has also been observed for graphene-filled composites and represents a serious hurdle to the production of high performance polymer–nanosheet composites.