There's a news article in the London Times that states (factually) that overcrowding in Scottish prisons is quite high (although it does not state capacity). What is eye opening is that the article then goes on to make the point that to reduce over crowding in the aforementioned Scottish prisons, the Government will have to start releasing prisoners early, imprisoning miscreants less and limit judicial sentencing discretion.
The authorities traveled to Finland and Ireland to study alternatives to prison. They also say they went to New York to study what the Yanks have been up to. They apparently did not pay attention to what the NY Correctional people told them.
Here's a tip. It's free, but true nonetheless. If you increase prison capacity and then incarcerate miscreants for the term of their sentences, and start imposing recidivism penalties as well, crime drops dramatically. Whatever the cost of imprisonment, having criminals loose in society committing crimes costs a great deal more.
The frugal thing to do is to build more prisons. That is the only way you have a chance of protecting your citizenry from theft and violence.