We have measured the equivalent width of the Ha emission line for 11 006 galaxies brighter than Mb, = -19 (ΩΛ = 0.7, Ωm = 0.3, H0 = 70 km s-1 Mpc-1) at 0.05 < z < 0.1 in the 2dF Galaxy Redshift Survey (2dFGRS), in the fields of 17 known galaxy clusters. The limited redshift range ensures that our results are insensitive to aperture bias, and to residuals from night sky emission lines. We use these measurements to trace μ*, the star formation rate normalized to L*, as a function of distance from the cluster centre, and local projected galaxy density. We find that the distribution of μ* steadily skews toward larger values with increasing distance from the cluster centre, converging to the field distribution at distances greater than ∼3 times the virial radius. A correlation between star formation rate and local projected density is also found, which is independent of cluster velocity dispersion and disappears at projected densities below ∼1 galaxy Mpc-2 (brighter than Mb, = -19). This characteristic scale corresponds approximately to the mean density at the cluster virial radius. The same correlation holds for galaxies more than two virial radii from the cluster centre. We conclude that environmental influences on galaxy properties are not restricted to cluster cores, but are effective in all groups where the density exceeds this critical value. The present-day abundance of such systems, and the strong evolution of this abundance, makes it likely that hierarchical growth of structure plays a significant role in decreasing the global average star formation rate. Finally, the low star formation rates well beyond the virialized cluster rule out severe physical processes, such as ram pressure stripping of disc gas, as being completely responsible for the variations in galaxy properties with environment.