Labour has said that male prisons are currently running at 99 per cent capacity and there will be "no spare cells" by November if nothing is done.
Justice Secretary Shabana Mahmood gave a Downing Street briefing "to set out the scale of the crisis" facing the prison service.
Director general chief executive at the service Amy Rees said the main problem is prisoners being recalled back to prison, adding that this has risen astronomically since the 1990s.
It comes as ex-prison officers have warned of conditions for frontline workers in British jails.
Justice Secretary Shabana Mahmood PARees said: "The total prison population is 88,087 and the adult male estate is operating at approximately 99 per cent of its capacity every year.
"On our current trajectory, the prison population rises by 3,000, and now we expect to hit zero capacity, to entirely run out of prison places for adult men, in November of this year."
The prison population is rising by 3,000 each year, "the equivalent of two large prisons every single year", Rees claimed.
She added: “Even with these measures in place, we will run out of prison places in just five months time."
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PALord Timpson told Sky News earlier today: "we should consider everything...Violence in prisons is too high.
"When you have prisons that are so full that the people are not going to education… you get more violence."
Meanwhile, chairman of the Prison Officers Association (POA) said building new prisons will not improve the current population crisis.
“The Government would be better off spending billions of taxpayers’ money on modernising the prison estate, funding an under-resourced probation service, providing more secure mental health beds and ensuring we have robust community sentences that the public have confidence in,” Mark Fairhurst said.
"Building new prisons will take years and will not improve the current population crisis...If new prisons are to be built, I hope the Labour Party’s commitment to the biggest insourcing in a generation is applied and the new build prisons remain in the public sector."
Responding to today's announcement, Mahmood's Conservative counterpart Robert Jenrick wrote on social media: "To govern is to choose. There are 10,350 foreign criminals in our jails. 17,000 people are awaiting trial.
"Instead of reducing those numbers, Labour have decided to let out criminals who reoffend early.
"They’re siding with criminals over the public. Labour’s Justice Secretary, Shabana Mahmood, has chosen to put the public at risk rather than deporting the foreign criminals who are clogging up our prisons."
