A stochastic backscatter (SB) approach to subgrid-scale (SGS) modelling for large-eddy simulation (LES) of the neutral atmospheric boundary layer (ABL) has previously been shown to reduce excessive velocity shear, as seen with the popular Smagorinsky SGS model, in the under-resolved surface layer. However, previous SB models exhibit unwanted grid-dependency issues, and the range of atmospheric flows tested remains limited. Here, a new SB model is proposed that uses a grid-adaptive filter to control the length-scale, anisotropy and momentum flux of the backscatter fluctuations, independently of the model grid. Model performance is confirmed to be grid-independent in simulations of the neutral ABL, in which an 80% reduction in excessive near-surface velocity shear is achieved. The model is also applied to street canyon flow, where the shear layer that separates the recirculating vortex within the canyon from the external flow is again typically under-resolved in most LES set-ups. The backscatter acts to increase momentum transfer across the shear layer, bringing the simulated vortex intensity significantly closer towards wind-tunnel observations. A passive tracer is also released to model traffic emissions, and the pollutant exchange velocity between the canyon and the external flow is again found in better agreement with wind-tunnel data. This information can be used to improve operational urban dispersion models.