ABSTRACT Observational measures of the primordial helium mass fraction, YP, are of interest for cosmology and fundamental particle physics. Current measures obtained from ${\text{H}\, \small {II}}$ regions agree with the Standard Model prediction to approximately 1 per cent precision, although these determinations may be affected by systematic uncertainties. This possibility can only be tested by independently measuring the helium abundance in new ways. Here, we propose a novel method to obtain a measurement of YP using hydrogen and helium recombination line emission from REionization-Limited HI Clouds (RELHICs): pristine, gas-rich but star-free low-mass dark matter haloes whose existence is predicted by hydrodynamical simulations. Although expected to be uncommon and intrinsically faint in emission, the primordial composition and simple physical properties of these objects make them an ideal laboratory to determine YP. We present radiative transfer simulations to demonstrate the effectiveness of this approach, finding that a comparison of the emission in H and He lines, either via their volumetric emissivities, or integrated properties such as the surface brightness and total flux, may be used to infer YP. Furthermore, we show that RELHICs can be used to provide an entirely novel constraint on the spectral slope of the ultraviolet background, and discuss the possibility of measuring this slope and the primordial helium abundance simultaneously.