There is no estimate at present. However, we are carrying out a longitudinal study of prisoners, Surveying Prisoner Crime Reduction (SPCR). This is designed to enhance our knowledge of the extent to which various factors relating to prisoners, including mental health problems, are linked with reoffending.
An initial report on SPCR, focusing simply on prisoner characteristics, including mental health, has been published by the Ministry of Justice, in 2008. This carries the title: The Problems and Needs of Newly Sentenced Prisoners: Results from a National Survey. Ministry of Justice Research Series 16/08 (2008).