Domestic cats are popular companion animals, however not all live in human homes and many cats live within shelters or as free-roaming, unowned- feral or stray cats. Cats can transition between these subpopulations, but the influence of this connectivity on overall population dynamics, and the effectiveness of management interventions, remain poorly understood. We developed a UK-focused multistate Matrix Population Model (MPM), combining multiple life history parameters into an integrated model of cat demography and population dynamics. The model characterises cats according to their age, subpopulation and reproductive status, resulting in a 28-state model. We account for density-dependence, seasonality and uncertainty in our modelled projections. Through simulations, we examine the model by testing the effect of different female owned-cat neutering scenarios over a 10-year projection timespan. We also use the model to identify the vital rates to which total population growth is most sensitive. The current model framework demonstrates that increased prevalence of neutering within the owned cat subpopulation influences the population dynamics of all subpopulations. Further simulations find that neutering owned cats younger is sufficient to reduce overall population growth rate, regardless of the overall neutering prevalence. Population growth rate is most influenced by owned cat survival and fecundity. Owned cats, which made up the majority of our modelled population, have the most influence on overall population dynamics, followed by stray, feral and then shelter cats. Due to the importance of owned-cat parameters within the current model framework, we find cat population dynamics are most sensitive to shifts in owned cat husbandry. Our results provide a first evaluation of the demography of the domestic cat population in the UK and provide the first structured population model of its kind, thus contributing to a wider understanding of the importance of modelling connectivity between subpopulations. Through example scenarios we highlight the importance of studying domestic cat populations in their entirety to better understand factors influencing their dynamics and to guide management planning. The model provides a theoretical framework for further development, tailoring to specific geographies and experimental investigation of management interventions.