The prison population in England and Wales has risen steeply since the mid-1990s, doubling in size between 1992 and 2012.
Shortly after coming into power, the Labour government, faced with warnings that prisons would run out of space within days, released thousands of inmates.
The Sentencing Act reduces the point of release meaning some prisoners could be let out after serving a third of their sentence, while those who would previously have served two-thirds will instead be released after serving half of their sentence.
The legislation also says courts should stop handing out short prison sentences of under a year, other than in specific or exceptional circumstances.
Katie Kempen, chief executive at Victim Support, said: “It’s encouraging to hear the new PM will be looking again at the early release policy.
“This review must urgently fix the fact that most victims currently have no way of knowing whether or not an offender could be released early.”
Conservative shadow justice minister Nick Timothy said: “Labour’s early release scheme has been catastrophic. Victims should not have to live in fear all summer waiting for a review.
“It would be shameful if the killers of PC Andrew Harper, grooming gang perpetrators and rapists were to get out of prison early, but this is what Labour had planned.”
There are just under 3,000 vacant spaces in prisons across England and Wales, more than this time two years ago when they were on the verge of reaching full capacity.
The Sentencing Act was created to help alleviate some of that pressure by letting out more than 5,000 inmates earlier than their potential release date so that more spaces would be created and staff weren’t overstretched.
If Burnham were to pull the plans, prison staff have told the BBC it could be “highly problematic”.
They had been expecting thousands to be released in the autumn under the new law – freeing up cells for people handed custodial sentences.
One senior prison staffer said “with such little headroom, we need more cells to put people in. Otherwise it’s going to get hairy again. We don’t want a repeat of 2024.”