The Asian tiger mosquito Aedes albopictus is able to transmit various pathogens to humans and animals and it has already caused minor outbreaks of dengue and chikungunya in southern Europe. Alarmingly, it is spreading northwards and its eggs have been found in the UK in 2016 and 2017. Climate-driven models can help to analyse whether this originally subtropical species could become established in northern Europe. But so far, these models have not considered the impact of the diurnal temperature range (DTR) experienced by mosquitoes in the field. Here, we describe a dynamical model for the life cycle of Ae. albopictus , taking into account the DTR, rainfall, photoperiod and human population density. We develop a new metric for habitat suitability and drive our model with different climate data sets to analyse the UK’s suitability for this species. For now, most of the UK seems to be rather unsuitable, except for some densely populated and high importation risk areas in southeast England. But this picture changes in the next 50 years: future scenarios suggest that Ae. albopictus could become established over almost all of England and Wales, indicating the need for continued mosquito surveillance.