The new Justice Secretary Ken Clarke is under pressure to put a freeze on the building of new prisons and to stop the record-level jail population from rising further.
Under Labour the overcrowding in prisons led to some 80,000 prisoners were let out under an early release scheme, which ended in March.
Just a month later, prison population levels reached record numbers at 85,076. The Conservatives then pledged in their election manifesto to increase jail capacity.
But the Prison Reform Trust (PRT) says that for each new prison place, it will cost the taxpayer £170,000, and have urged the government to find an alternative solution.
Director of the PRT Juliet Lyon said: "The current growth in prison numbers is unsustainable.
"A moratorium on prison building would be a first step in reversing the disastrous legacy of the past two decades which has seen the prison population almost double, while rates of reoffending have rocketed.
"A measured, evidence-based approach to justice would deliver the prize of increasing public safety while at the same time reducing the cost burden imposed by over-use of imprisonment."
In response the Ministry of Justice said: "This is an interesting and timely contribution to the debate on prison reform.
"Prisons are an extremely important part of our criminal justice system. They must be used effectively for the protection of the public while giving prisoners the best possible chance of being rehabilitated and increasing the likelihood of them leading law-abiding lives when they are released."