ABSTRACT The accurate flux calibration of observational data is vital for astrophysics and cosmology because absolute flux uncertainties of stellar standards propagate into scientific results. With the ever higher precision achieved by telescopic missions (e.g. JWST) in the infrared (IR), suitable calibrators are required for this regime. The basis of the Hubble Space Telescope (HST) flux scale is defined by model fits of three hot (${T_\mathrm{eff}} > 30\, 000$ K) hydrogen-atmosphere (DA) white dwarfs, which achieve an accuracy better than 1 per cent at optical wavelengths but falls below this level in the IR range. We present a network of 17 cooler DA white dwarfs with ${T_\mathrm{eff}} < 20\, 000$ K as spectrophotometric flux standards that are equally, if not more, accurate at IR wavelengths. Cooler white dwarfs do not suffer from non-local thermal equilibrium effects in continuum flux or from ultraviolet metal line blanketing, have a larger sky density, are generally closer to Earth with little or negligible interstellar reddening, and have energy distributions peaking in the optical or near-IR. Using the latest grid of DA local thermal equilibrium atmosphere models with three-dimensional convection, the observed Space Telescope Imaging Spectrometer (STIS) and Wide Field Camera 3 (WFC3) fluxes of our network are accurate to 3 per cent over most of the range $1450\!\! - \!\!16\, 000$ Å, with a median standard deviation of 1.41 per cent. Fitting the HST STIS and WFC3 white dwarf spectral energy distributions (SEDs) and Balmer lines independently yields SEDs that agree within $3\sigma$, which demonstrates the precision of the models for our network.