There are fewer than 350 prison places available in England and Wales, including spaces made available in prison cells.
The prison population has reached a record high of 80,812, having risen by 154 since last week.
Taking into account the 400 police cells created by Operation Safeguard, there are 320 prison places remaining. Operation Safeguard was launched in October 2006 to make police cells available to ease prison overcrowding.
Prison services were removed from the Home Office to the newly formed Ministry of Justice (MoJ) on May 9th, presenting the lord chancellor Lord Falconer with the immediate challenge of stemming the prison service.
Justice minister David Hanson said the ministry would look "imaginatively" at how alternative sentences could be introduced. The MoJ is expected to review sentencing, consider a cap on sentences and reconsider the crimes punishable by suspended sentences.
But, he told the BBC the rising prison population should be seen as a sign more crimes are being solved and mean the ministry is protecting the public.
Shadow home secretary David Davis argued, however, that prison overcrowding would mean offenders who should be incarcerated are not sent to prison.
He said: "Prison rehab and skills courses are disrupted and prisoners are let out early. Ultimately, it is the public who pay the price."
Ms Davis said the government had been warned of a prison crisis for years, and had "recklessly" ignored their own projections on prison overcrowding.
The Home Office says more than 20,000 prison places have been made available since 1997 and there are plans for a further 8,000 over the next five years.