Context. The shape of the ionising spectra of galaxies is a key ingredient to reveal their physical properties and for our understanding of the ionising background radiation. A long-standing unsolved problem is the presence of He II nebular emission in many low-metallicity star-forming galaxies. This emission requires ionising photons with an energy > 54 eV; it is important to note that these particular photons are not produced in sufficient amounts by normal stellar populations.Aims. To examine if high mass X-ray binaries and ultra-luminous X-ray sources (HMXBs and ULXs) can explain the observed He II nebular emission and how their presence alters other emission lines, we computed photoionisation models of galaxies including such sources.Methods. We combined spectral energy distributions (SEDs) of integrated stellar populations with constrained SEDs of ULXs to obtain composite spectra with varying amounts of X-ray luminosity, parameterised by LX/SFR. With these, we computed photoionisation models to predict the emission line fluxes of the optical recombination lines of H and He+, as well as the main metal lines of [O III], [O II], [O I], and [N II]. The predictions were then compared to a large sample of low-metallicity galaxies.Results. We find that it is possible to reproduce the nebular He II λ4686 and other line observations with our spectra and with amounts of LX/SFR compatible with the observations. Our work suggests that HMBXs and ULXs could be responsible for the observed nebular He II emission. However, the strengths of the high and low ionisation lines, such as He II and [O I] λ6300, strongly depend on the X-ray contribution and on the assumed SEDs of the high energy source(s), the latter being poorly known.Key words: galaxies: ISM / galaxies: high-redshift / X-rays: binaries / radiation mechanisms: general