We measure how the properties of star-forming central galaxies correlate with large-scale environment, d, measured on 10 h-1 Mpc scales. We use galaxy group catalogues to isolate a robust sample of central galaxies with high purity and completeness. The galaxy properties we investigate are star formation rate (SFR), exponential disc scale length Rexp, and Sersic index of the galaxy light profile, nS. We find that, at all stellar masses, there is an inverse correlation between SFR and δ, meaning that above-average star-forming centrals live in underdense regions. For nS and Rexp, there is no correlation with δ at M* ≲ 1010.5 M⊙, but at higher masses there are positive correlations; a weak correlation with Rexp and a strong correlation with nS. These data are evidence of assembly bias within the star-forming population. The results for SFR are consistent with a model in which SFR correlates with present-day halo accretion rate, Mh. In thismodel, galaxies are assigned to haloes using the abundance-matching ansatz, which maps galaxy stellar mass onto halo mass. At fixed halo mass, SFR is then assigned to galaxies using the same approach, but Mh is used to map onto SFR. The best-fitting model requires some scatter in the Mh-SFR relation. The Rexp and nS measurements are consistent with a model in which both of these quantities are correlated with the spin parameter of the halo, λ. Halo spin does not correlate with δ at low halo masses, but for higher mass haloes, high-spin haloes live in higher density environments at fixed Mh. Put together with the earlier instalments of this series, these data demonstrate that quenching processes have limited correlation with halo formation history, but the growth of active galaxies, as well as other detailed galaxies properties, are influenced by the details of halo assembly.