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There is increasing concern about the lack of accuracy in population projections at national levels. A common problem has been the systematic underestimation of improvements in mortality, especially at older ages, resulting in projections that are too low. In this paper, we present a method that is based on projecting survivorship rather than mortality, which uses the same data but differs technically. In particular, rather than extrapolating trends in mortality, we use trends in life expectancy to establish a robust statistical relation between changes in life expectancy and survivorship using period life tables. We test the approach on data for England and Wales for the population aged 50 and over, and show that it gives more accurate projections than official projections using the same base data. Using the model to project the population aged 50 and over to 2020, our method suggests nearly 0.6 million more people in this age group than official projections. [ABSTRACT FROM PUBLISHER]