Agricultural expansion and intensification have resulted in strong declines in farmland biodiversity across Europe. In many intensively farmed landscapes, linear landscape elements such as field boundaries, road verges and ditch banks are the main remaining green infrastructures providing refuge for biodiversity, and as such play a pivotal role in agri‐environmental policies aiming at mitigating biodiversity loss. Yet, while we have a fairly good understanding of how agricultural intensification influences biodiversity on farmland, little is known about whether and how local land‐use intensity affects biodiversity in nearby linear landscape elements and how this affects their role as biodiversity refuge. Focussing on pollinating insects, we examined the effects of local land‐use intensity on biodiversity in agricultural fields and adjacent green infrastructures. In an intensively farmed area in south‐western France, we selected 23 agricultural grasslands and nearby field boundaries along a gradient in grassland cutting frequency which acted as a proxy for land‐use intensity. We analysed how grassland cutting frequency affects species richness, abundance and community composition of wild bees and hoverflies in the grasslands and neighbouring field boundaries, and whether these effects differ across habitat types and species groups. Grassland cutting frequency negatively affected pollinator species richness and abundance in the grasslands, whereas pollinators in the neighbouring field boundaries were unaffected. These responses reflected the effects of cutting frequency on floral resources, with flower cover and richness decreasing in grasslands but not in field boundaries. As a result, the proportion of the local pollinator community supported by field boundaries increased with the increasing cutting frequency of the adjacent grassland. Common and rare pollinator species generally showed similar responses. Furthermore, communities of plants and pollinators in field boundaries next to intensively farmed grasslands were fairly similar to those next to extensively farmed ones. Synthesis and applications . Our results suggest that, as nearby land use intensifies, flower‐rich field boundaries become increasingly important as pollinator refuge habitats. Conserving field boundaries and other green infrastructures, and maintaining or enhancing their quality, therefore constitute important tools to conserve and promote pollinators in intensively farmed landscapes.