We augment the well-known susceptible - infected - recovered - deceased (SIRD) epidemiological model to include vaccination dynamics, implemented as a piecewise continuous simulation. We calibrate this model to reported case data in the UK at a national level. Our modelling approach decouples the inherent characteristics of the infection from the degree of human interaction (as defined by the effective reproduction number, Re). This allows us to detect and infer a change in the characteristic of the infection, for example the emergence of the Kent variant, We find that that the infection rate constant (k) increases by around 89% as a result of the B.1.1.7 (Kent) COVID-19 variant in England. Through retrospective analysis and modelling of early epidemic case data (between March 2020 and May 2020) we estimate that ~1.2M COVID-19 infections were unreported in the early phase of the epidemic in the UK. We also obtain an estimate of the basic reproduction number as, R0=3.23. We use our model to assess the UK Government's roadmap for easing the third national lockdown as a result of the current vaccination programme. To do this we use our estimated model parameters and a future forecast of the daily vaccination rates of the next few months. Our modelling predicts an increased number of daily cases as NPIs are lifted in May and June 2021. We quantify this increase in terms of the vaccine rollout rate and in particular the percentage vaccine uptake rate of eligible individuals, and show that a reduced take up of vaccination by eligible adults may lead to a significant increase in new infections.