Neutron reflectometry (NR) is a powerful technique for interrogating the structure of thin films at interfaces. Because NR measurements are slow and instrument availability is limited, measurement efficiency is paramount. One approach to improving measurement efficiency is active learning (AL), in which the next measurement configurations are selected on the basis of information gained from the partial data collected so far. AutoRefl, a model-based AL algorithm for neutron reflectometry measurements, is presented in this manuscript. AutoRefl uses the existing measurements of a function to choose both the position and the duration of the next measurement. AutoRefl maximizes the information acquisition rate in specific model parameters of interest and uses the well defined signal-to-noise ratio in counting measurements to choose appropriate measurement times. Since continuous measurement is desirable for practical implementation, AutoRefl features forecasting, in which the optimal positions of multiple future measurements are predicted from existing measurements. The performance of AutoRefl is compared with that of well established best practice measurements for supported lipid bilayer samples using realistic digital twins of monochromatic and polychromatic reflectometers. AutoRefl is shown to improve NR measurement speeds in all cases significantly.