Supplementary feeding of birds, particularly in urban areas, is often associated with increased population size and fecundity. In the UK, the non‐native Grey Squirrel Sciurus carolinensis is common in rural and urban habitats. It exploits supplementary feeders and may induce interference competition by excluding birds, but empirical evidence of this is unavailable. Using controlled model presentation experiments, we demonstrate that Grey Squirrels could reduce bird use of supplementary feeders and induce interference competition. Total bird resource use was reduced by 98% and most species exhibited similar sensitivities. The likelihood and magnitude of interference competition will depend on how rapidly displaced birds find alternative food sources; it will be greatest where there are high Grey Squirrel densities and few supplementary feeders. Other studies suggest that supplementary feeding increases Grey Squirrel numbers, and the species is also predicted to expand its non‐native range across most of Europe. Our data indicate that Grey Squirrels may eventually alter the net effect of supplementary feeding on bird populations across the European continent; increased use of squirrel‐proof feeders may help to minimize such effects.