NHS Psychiatric beds comprise mental illness and intellectual disability beds. Penrose hypothesised that the number of psychiatric in-patients was inversely related to prison population size.

To ascertain whether the Penrose hypothesis held true in England between 1960 and 2018–2019.

A time-series analysis explored the association between total prison population and NHS psychiatric beds; this was also tested for the male and female prison populations, using non-psychiatric beds as a comparator. Associations were explored with time lags of up to 20 years. Linear regression was conducted to estimate the size of the effect of bed closures.

NHS psychiatric beds decreased 93% and the prison population increased 208%. A strong (r =−0.96) and highly significant negative correlation between these changes was found. Annual reduction in psychiatric bed numbers was associated with an increase in prison population, strongest at a lag of 10 years. The closure of mental illness and intellectual disability beds was associated with increases in female prisoners 10 years later. The only significant explanatory variable for the increase in male prison population was intellectual disability bed reduction.

The Penrose hypothesis held true between 1960 and 2018–2019 in England: psychiatric bed closures were associated with increases in prison population up to 10 years later. For every 100 psychiatric beds closed, there were 36 more prisoners 10 years later: 3 more female prisoners and 33 more male prisoners. Our results suggest that the dramatic increase in the female prison population may relate to the closure of NHS beds.