Disc reverberation mapping of a handful of nearby active galactic nuclei (AGNs) suggests accretion disc sizes that are a factor of a few too large for their luminosities, apparently at odds with the standard model. Here, we investigate the likely contribution to the measured delay signature of diffuse continuum emission arising from broad-line region gas. We start by constructing spherically symmetric pressure-law BLR models (i.e. P(r)∝r-s) that approximately reproduce the observed emission line fluxes of the strong UV-optical emission lines in the best-studied source, NGC 5548. We then determine the contribution of the diffuse continuum to the measured continuum flux and inter-band delays, accounting for the observed variability behaviour of the ionizing nuclear continuum. Those pressure-law models that approximately reproduce the observed emission-line luminosities unavoidably produce substantial diffuse continuum emission. This causes a significant contamination of the disc reverberation signature (i.e. wavelength-dependent continuum delays). Qualitatively, the diffuse continuum delay signatures produced by our models resemble that observed for NGC 5548, including the deviation of the lag spectrum above that of a simple power law in wavelength, short-ward of the Balmer and Paschen jumps. Furthermore, for reasonable estimates of the BLR covering fraction, the delay induced by diffuse continuum emission causes elevated inter-band delays over the entire UV-optical regime; for these pressure-law models, there are no `disc-dominated' wavelength intervals. Thus, the diffuse continuum contribution must be taken into account in order to correctly infer AGN accretion disc sizes based on inter-band continuum delays.