Relatively little is known about the factors behind the gross level of international migrant flows into the UK, despite the rapid growth in the number of migrants seen in recent years. This matters because assumptions about the future evolution of migration are an important component of official judgements about the potential trend rate of economic growth. In this paper we develop the first detailed econometric model of the economic and demographic determinants of annual migrant inflows into the UK from a number of different locations. Some of the factors found to be important, such as Ôfriends and family' effects from existing migrants, income differentials between the host and source location and the demographic structure of the source location population, have been shown to matter in other host economies as well. But we also show that it is important to allow both for developments in other potential host locations and for heterogeneity in the speed with which migration from different source locations responds to changes in economic circumstances. Neither of these factors have been given much attention to date in the applied literature on international migration. We find that the change in migration over the decade to 1998-2000 is primarily due to population growth in the source locations and the continuing pull effects from the rise in the migrant stock and per capita incomes in the UK relative to the source location.