After reading accounts of prison life by former inmates, and accounts by police officers who have to deal with reoffenders, I think it's pretty clear that prisons in this country do need some pretty major changes.
Firstly, people in prison still have access to drugs and alcohol, so their problems with them are less likely to stop. It's more expensive, but people can still find a way to get it. From one prisoner's account, it's mostly smuggled in by a small number of guards as well, along with mobile phones.
Secondly, on release, people don't get enough support. If somebody's dumped by the roadside with only the possessions they came into prison with, after possibly losing their home and job and contacts and stuff while they were inside, then they probably will be pushed back towards reoffending just to make ends meet.
Thirdly, if we gave the probation service some money then they could try to do more to help people with drug and alcohol problems when they were released, rather than making them sign in once a week or however often it is.
Fourthly, the CPS could push for (and the magistrates could provide) longer sentences for repeat offenders. I've heard of cases where people who had reoffended on release were arrested and sent back to prison for a couple of months, were released, reoffended and got another two month sentence. Again and again and again. After a certain point, prison sentences stop being a deterrent and just become a way to give the local police a break from arresting somebody from a couple of months, and the people committing these crimes (especially in the case of acquisitive crime) still aren't getting any help dealing with addictions or mental health issues.I think that our prison and justice system does very little to deter people from reoffending, and leaves it all up to family and friends, charities and to some extent the police and social services.