Justice Secretary Chris Grayling has said he is taking "sensible steps" to deal with a rise in prisoner numbers after it was reported that 34 full and overcrowded jails are being told to make room for more offenders.
Labour said the news that 40 institutions - all but six already at full capacity or beyond - need to find room for extra inmates is t he consequence of the Government's decision to shut 17 other jails, and accused ministers of "incompetence".
But Mr Grayling said he was simply using "spare capacity" to deal with a small increase - and was also recruiting up to 100 prison officers on short-term contracts - and would "make no apology" that more criminals were being put behind bars.
The BBC said it had seen documents which showed the prisons in England and Wales had been told to raise their "operational capacity" in the next two months to accept 440 more inmates between them.
Bedford, Durham, Leeds, Leicester, Lincoln, Brixton, Pentonville and Wandsworth are said to be among those affected.
Shadow justice secretary Sadiq Khan said: "David Cameron must accept that the decision to close down 17 prisons was wrong. Because of his ministers' incompetence they've created an acute shortage of space.
"Things are so bad they've had to resort to holding prisoners in police cells and they've moved serious and violent prisoners into open jails.
"Their latest desperate measure is to stuff more and more prisoners into already dangerously overcrowded prison cells.
"But a quart into a pint pot won't go. This type of environment will do nothing to rehabilitate prisoners or to reduce crime and is yet another example of the Government failure in this area."
Mr Grayling hit back: "We have had a small increase in prison population in the last few months. And as a result, we've opened up some of our reserve capacity.
"To do this we are planning to take on a number of former prison officers - up to 100 - on short-term contracts. We're also opening 2,000 additional adult male prison places over the next nine months as part of my commitment to ensure we go into the next election with more adult male places than we inherited in 2010."
He went on: "I make no apology that we are sending more criminals to prison - that's what the public want. I'm just taking sensible steps to make sure we can accommodate everyone the court sends to us.
"I'll take no lessons on this issue from the Labour Party who let thousands of dangerous prisons out on to our streets early because they failed to provide enough places."
Juliet Lyon, director of the Prison Reform Trust, said: " Instead of indulging in political mudslinging, ministers and Opposition shadows must wake up to the damage they are doing to a respected public service.
"Prisons are struggling against a tide of rising prison numbers, budget cuts, reduced staffing levels, recruitment and sickness problems and an increase in serious assaults and suicide in custody.
"Solutions lie not in warehousing more people or exploiting fear of crime but in authoritative leadership to ensure that offenders make amends to victims, break addictions and take responsibility for their lives.
"One look at prison reconviction rates - half of all prisoners reconvicted within one year of release - would show any sensible person that cramming more and more people into bleak prison cells is no way to reduce reoffending."
Labour has also called for a spending watchdog investigation into the Government's decision to pay for an additional 412 places this year so far in privately-run prisons to help address pressures.
Prisons Minister Jeremy Wright revealed in an answer to a parliamentary question tabled by Mr Khan that the places had been secured for between six and 11 months - but declined to reveal the cost to the taxpayer.
Mr Wright said that information was "commercially sensitive".
But Mr Khan suggested that the Government was "embarrassed" to admit the amount it had paid and he has written to the chair of the Commons Public Accounts Committee - Labour MP Margaret Hodge - requesting an investigation.
"This shortage of space is a crisis of the Government's making, and as a result of their actions they have had to resort to the emergency step of buying extra spaces from private providers," he told her.
"This is an option of last resort and is known to be very costly.
"My concern is that the true cost of the Government's actions is being withheld from the public simply to hide ministers' embarrassment at this crisis being one they created. This is unacceptable."
A recent report by the committee criticised the handling of the prison closure programme.