This short paper studies a simple Malthusian model with perpetually growing productivity. The model is calibrated to match the British growth record from 1270 to 1650, and, then, to 1870. Results are as follow: (i) Both the Black Death and perpetually growing productivity have explanatory power for preindustrial prosperity. (ii) For the extended Malthusian model to match the data from 1270 to the mid-17th century, the production technology must be extremely labor intensive. (iii) The model cannot capture the growth acceleration after the mid-17th century even with unrealistic parameter values. These results imply that the British economy was in a distinct Post-Malthusian regime in the post1650 period, and they substantiate the strong relevance of Unified Growth Theory to the British economic development over the very long run.