Glassy polymers exhibit a constitutive response that is non-linear viscoelastic for all but small strains and make for a challenging set of materials to model. Mechanical properties are highly dependent on test conditions such as strain rate and temperature and deviate further at high strain rates due to the onset of the beta transition and to adiabatic effects. Thus, to accurately model impact conditions where a component may experience a range of rates and temperatures, a single model is needed that can predict this response comprehensively across a very wide range of conditions. In this work we focus on the development of a constitutive model and its parameterisation for typical glassy polymers, using experimental data recently acquired through a range of techniques by collaborators at the University of Oxford. The constitutive equations of the Oxford glass-rubber constitutive model (1) were further developed with particular emphasis on the large strain response and the evolution of structure. Thus at short range the model encompasses a non-linear viscoelastic response with physical ageing and mechanical rejuvenation using the fictive temperature, and separate alpha and beta relaxations. At long range a temperature and rate dependent Edwards-Vilgis model captures the hyperelastic behaviour due to stretching of the entanglement network. Adiabatic heating is calculated accounting for dissipated energy, entropy-elasticity, and the energy needed for structural change. The model is parameterised using standard mechanical, thermomechanical and thermal experimental data across the broad range of test conditions (-60°C