Context. Time-delay lensing is a powerful tool for measuring the Hubble constant H0. However, in order to obtain an accurate estimate of H0 from a sample of time-delay lenses, very good knowledge of the mass structure of the lens galaxies is needed. Strong lensing data on their own are not sufficient to break the degeneracy between H0 and the lens model parameters on a single object basis. Aims: The goal of this study is to determine whether it is possible to break the H0-lens structure degeneracy with the statistical combination of a large sample of time-delay lenses, relying purely on strong lensing data with no stellar kinematics information. Methods: I simulated a set of 100 lenses with doubly imaged quasars and related time-delay measurements. I fitted these data with a Bayesian hierarchical method and a flexible model for the lens population, emulating the lens modelling step. Results: The sample of 100 lenses on its own provides a measurement of H0 with 3% precision, but with a −4% bias. However, the addition of prior information on the lens structural parameters from a large sample of lenses with no time delays, such as that considered in Paper I, allows for a 1% level inference. Moreover, the 100 lenses allow for a 0.03 dex calibration of galaxy stellar masses, regardless of the level of prior knowledge of the Hubble constant. Conclusions: Breaking the H0-lens model degeneracy with lensing data alone is possible, but 1% measurements of H0 require either many more than 100 time-delay lenses or knowledge of the structural parameter distribution of the lens population from a separate sample of lenses.