The mass assembly history of the Milky Way can inform both theory of galaxy formation and the underlying cosmological model. Thus, observational constraints on the properties of both its baryonic and dark matter contents are sought... Here we show that hypervelocity stars (HVSs) can in principle provide such constraints. We model the observed velocity distribution of HVSs, produced by tidal break-up of stellar binaries caused by Sgr A*. Considering a Galactic Centre (GC) binary population consistent with that inferred in more observationally accessible regions, a fit to current HVS data with significance level > 5\% can only be obtained if the escape velocity from the GC to 50 kpc is $V_G < 850$ km/s, regardless of the enclosed mass distribution. When a NFW matter density profile for the dark matter halo is assumed, haloes with $V_G < 850$ km/s are in agreement with predictions in the $\Lambda$CDM model and that a subset of models around $M_{200} \sim 0.5-1.5 \times 10^{12}$ solar masses and $r_s < 35$ kpc can also reproduce Galactic circular velocity data. HVS data alone cannot currently exclude potentials with $V_G > 850$ km/s. Finally, specific constraints on the halo mass from HVS data are highly dependent on the assumed baryonic mass potentials. This first attempt to simultaneously constrain GC and dark halo properties is primarily hampered by the paucity and quality of data. It nevertheless demonstrates the potential of our method, that may be fully realised with the ESA Gaia mission. (read more)