Abstract There is a global requirement to improve the environmental sustainability of intensively managed grassland monocultures that rely on high rates of nitrogen fertiliser, which is associated with negative environmental impacts. Multi‐species grass–legume mixtures are a promising tool for stimulating both productivity and sustainability in intensively managed grasslands, but questions remain about the benefit of increasing the diversity of plant functional groups. We established a plot‐scale experiment that manipulated the diversity of plant communities from a six‐species pool comprising three functional groups: grasses, legumes and herbs (two species each). Communities were grown as monocultures, or mixtures of two to six species, following a simplex design. This allowed us to quantify species’ identity effects and functional group interaction effects. To investigate the impact of severe weather events, main plots were split and two levels of water supply, ‘rainfed’ and a 2‐month experimental drought, were applied. Mineral nitrogen fertiliser was applied at 150 kg ha−1 year−1, and a Lolium perenne monoculture received 300 kg ha−1 year−1 (300N) as a highly fertilised comparison. Annual above‐ground biomass was measured for 2 years. We found a strong positive effect on yield due to functional group interactions. Multi‐species communities with three functional groups yielded more than the best‐performing monoculture over a large range of different relative abundances of the three functional groups. The highest diversity community outperformed the 300N L. perenne under rainfed conditions. Although species' monoculture yields were generally reduced by the experimental drought, the interaction effects were not affected by drought and remained sufficiently large for the six‐species mixture under drought to have similar yields to both the best‐performing monoculture and the 300N L. perenne under rainfed conditions. Synthesis and applications. Plant diversity can result in higher yields, mitigate the yield risks associated with extreme weather events and displace fertiliser inputs and their embedded greenhouse gas emissions. Multi‐species swards offer a practical, farm‐scale management action to enhance the sustainability of intensive grassland production.