The opposition frontbencher made the call during a debate on prisons and probation, as Labour called for no new contracts to be handed out to private contractors.
But Justice Secretary David Gauke hit back, saying the scheme had been a success overall, and attacking his opposite number’s “dogmatic” speech.
Mr Burgon said problems at HMP Birmingham, which was run by G4S before being taken back into the public sector, are not localised.
He added: “G4S has in fact failed across the justice sector. It has been forced to give up youth prisons after abuse allegations.
“Horrific treatment at its immigration detention centres has been exposed and the security giant is still under investigation by the Serious Fraud Office for its role in an electronic tagging scandal that included charging for dead people.
“Let’s be honest, its role in our justice system should be suspended and should have been suspended there and then, but the Government actually appears to be in hock to it and no wonder given that it has £5 billion of Ministry of Justice contracts.”
Labour’s opposition day motion is non-binding on the Government and simply expresses the opinion of the Commons.
It calls on the Government to end its plans to sign new private probation contracts and contracts for new privately run prisons.
Mr Burgon accused the Government of “throwing more good money after bad”, adding: “Just how bad does it have to get before the Conservative Party ends its obsession with the private sector?
“Private firms could be deliberately understaffing prisons to boost their profits. It’s clearly in the public interest that the staffing levels in private prisons are routinely published just as they are routinely published in publicly run prisons.”
He also called for an independent inquiry into whether privatisation has increased violence in prisons.
Mr Burgon finished by saying: “The Conservatives promised that privatisation of our justice system would lead to better services and lower costs. The evidence is now in, it has achieved neither.
“Instead of savings we’ve had bailouts, instead of improved safety there’s disproportionate violence, instead of accountability we’ve had secrecy.”
Mr Gauke said it was right to discuss the use of the private sector in prisons, but the Labour frontbencher’s speech was “simplistic, dogmatic and bombastic”.
He acknowledged that HMP Birmingham was a “failing prison” and standards were “unacceptable” during a 2018 inspection.
But he said the Government stepped in “at no extra cost to the taxpayer” and showed “when it is right to step in, we will step in”.
He added there are lots of other privately run prisons which have been a success, praising HMP Bronzefield, which has pioneered the use of in-cell phones for inmates, citing it as an example of the private sector “getting there first”.
Mr Gauke finished by saying: “We will always work to put the public first, in reducing reoffending, protecting the public and building a stronger justice system.”
Labour MP Mohammed Yasin (Bedford) said publicly run prisons are being “deliberately run into the ground and deprived of adequate funding”.
He added: “Marketisation has utterly failed in the prison and probation services and public safety has been compromised.
“It is time the Government listened to frontline workers who know exactly how to turn things around.”
Liberal Democrat Vera Hobhouse (Bath) said the Government should invest in women’s centres to help reduce reoffending.
She added: “Short sentences target the most vulnerable offenders, especially women, with 72% of women offenders being sentenced for less than a year.
“Sixty-two percent of these women sentenced for less than a year go on to reoffend. Often these months in prison are just enough time for a woman to lose her job, house and children.
“They find themselves released back into society with no safety nets and very little in the way of support.”