Real house prices rise in the United Kingdom amid growing concern of an impending correction. The rate of household formation has increased with strong population growth, due to elevated rates of natural increase and net migration, and lack of growth in average household size, due to a rise in single-person households with population ageing. This paper presents an overlapping generations model of housing, endogenous labour, savings and growth to analyse the effect of an increase in the household formation rate and speculative demand under rational expectations on house prices in a general equilibrium. We find that real house prices rise over time if the rate of household formation outstrips the rate of housing supply, but do not follow a speculative bubble path in the long run. The results explain why the upward trend in real house prices reflects market fundamentals and has continued despite population ageing as the number of working and retired households grows relative to the number of older people seeking to sell.