According to an article from 5 years ago, BBC NEWS | UK | Prison overcrowding 'at crisis point'. Apparently it still is: BBC NEWS | UK | UK Politics | Jail system in 'serious crisis'.
This "perpetual crisis" is simply a queueing problem: There is an arrival rate of prisoners (how many people we jail), there is a departure rate (how many people we release), and there is a storage capacity (how many we keep behind bars). To relieve this perpetual crisis, we can
1) reduce arrivals
2) increase departures
3) increase storage, either by adding capacity or making better use of the space through double or triple bedding.
The various strategies have been tried, reducing arrivals most notably last week when the beleagured Home Secretary (Attorney General/Secretary of Homeland Security more or less for US readers) was chastised by a judge who refused to jail a paedophile because of a memo from the Home Office about prison crowding.
Capacity will take some time to expand, especially given the inaction to date.
We could increase departures, but then prisoners would not serve their full sentences (and we know that prisoners who are safe to release after 7 years must somehow remain very dangerous after 6 years and 364 days).
The problem in thinking about this is the implicit (and wrong) assumption of inelasticity of demand, if we changed the cost, we would get just as many prisoners.
So how about pricing? Charging prisoners for their stay would probably not work, most can't afford it, and we would have to send them to debtor's prison.
Maybe we could charge someone else.
Prison cells are a scarce commodity, valuable to the communities seeking to send more of their own into the slammer. Each community (via their judges) would administer a "prison budget". The judges could bid on cells in an auction (envision eBay), perhaps a Dutch auction, for each of their potential prisoners, the highest N bidders get to imprison their least favorite baddies. There would of course be different classes of prison cells, and a certain number enter the market each week (e.g. 5 cells of maximum security with a 6 year stay, 19 cells of medium security for a 3 year stay). We might even get an options market, and trading between communities if the match didn't work. Prisons could transform security levels to better match market demand. It shouldn't take too long for a new equilibrium to emerge.
This might open up the option for new suppliers to enter the market, driving down costs. I don't know the legal nicities of this over here in the UK, but in the US many states have private prisons, and one could easily see the least dangerous baddies condemned to an underperforming Motel 6 instead of prison.
Communities would reveal through this process which crimes they really dislike based on how much they are willing to pay to imprison different people who committed different crimes.
Just a thought.