We test the Higgs dilaton inflation model (HDM) using the latest cosmological datasets, including the cosmic microwave background temperature, polarization and lensing data from thePlancksatellite (2015), the BICEP and Keck Array experiments, the type Ia supernovae from the JLA catalogue, the baryon acoustic oscillations from CMASS, LOWZ and 6dF, the weak lensing data from the CFHTLenS survey and the matter power spectrum measurements from the latest SDSS data release. We find that the values of all cosmological parameters allowed by the HDM are well within thePlancksatellite (2015) constraints. In particular, we determine,,,and(at 95.5% c.l.). We also place new stringent constraints on the couplings of the HDM,ξχ<0.00328 and(at 95.5% c.l.). We find that the HDM is only slightly better than thew0waCDM model, with. Given that the HDM has two fewer parameters, we find Bayesian evidence favouring the HDM over thew0waCDM model. We also study the critical Higgs inflation model, taking into account the running of both the self-coupling λ(μ) and the non-minimal coupling to gravityξ(μ). We find peaks in the curvature power spectrum at scales corresponding to the critical valueμthat re-enter during the radiation era and collapse to form a broad distribution of clustered primordial black holes, which could constitute today the main component of dark matter.This article is part of the Theo Murphy meeting issue ‘Higgs cosmology’.