A criminal investigation has been opened into government electronic tagging contracts held with Serco, as well as G4S, the Serious Fraud Office (SFO) said.
An audit by accountancy firm PricewaterhouseCoopers, launched in May, alleged that overcharging began at least as far back as the start of the current contracts in 2005 but could have dated back to 1999.
Justice Secretary Chris Grayling told the two firms that an independent forensic audit was required to look at internal email trails between executives to establish what happened. While Serco agreed to take part, G4S refused.
Serco allowed a further forensic audit to take place but G4S refused to co-operate and were reported to the SFO.
A criminal investigation has been launched into a contract between security firm G4S and the Government for tagging criminals.
An inquiry has been opened by the Serious Fraud Office after it emerged G4S, along with Serco, had charged the Ministry of Justice for monitoring offenders who were dead, back in prison, had their tags removed, left the country or never been tagged in the first place.
An audit by accountancy firm PricewaterhouseCoopers, launched in May, alleged that overcharging began at least as far back as the start of the current contracts in 2005.
Two staff at a privately-run immigration removal centre for women have been fired for engaging in sexual activity with a detainee.
A third employee at the Serco-operated Yarl's Wood, in Bedfordshire, was also sacked for failing to take any action when the female detainee reported the two men, HM Chief Inspector of Prisons Nick Hardwick said.
Last month it was reported police were investigating claims that a 23-year-old Roma woman who was held at Yarl's Wood was subject to inappropriate sexual behaviour from guards.
But inspectors found no evidence that a "wider culture of victimisation or systematic abuse" had developed following the new allegations of abuse at the 400-bed centre.
Christopher Hyman, the chief executive of security giant Serco, which is facing an investigation after the Government was overcharged millions of pounds for electronically tagging criminals, has resigned, the company announced.
Private security firm Serco "absolutely refutes" any allegations of sexual misconduct between staff and inmates, says the man running the main removal centre for women in the UK.
Police are examining accusations of sexual contact with guards at Yarl's Wood made by a 23-year-old former inmate.
Serco absolutely refutes the allegations made that there is an environment at Yarl's Wood where sexual intimidation or inappropriate behaviour is in any way tolerated.
We have strict procedures for dealing with any such complaints and they are always fully investigated...
On the occasion when an complaint of sexually inappropriate behaviour between staff and a resident was brought to our attention in 2012 the matter was properly investigated and the police were kept fully informed throughout. As a result three members of staff were dismissed.
– Director of Yarl's Wood immigration removal centre John Tolland
Responding to allegations of sexual contact between guards and a former inmate, the Home Office said any claims of misconduct would be "thoroughly investigated".
They take the welfare of detained asylum seekers "very seriously" and expect private security firms working on their behalf to "maintain the highest standards".
We take the welfare of our detainees very seriously. Detention and removal are essential parts of effective immigration controls, but it is vital that these are carried out with humanity and dignity, and we are committed to ensuring that this is the case.
We expect contractors to maintain the highest standards. Any allegations of misconduct are thoroughly investigated and, if necessary, they will be reported to the appropriate authorities, including the police.
There should be a "full and thorough" investigation into claims of inappropriate sexual behaviour at the largest immigration removal centre for women in UK, the Shadow Home Secretary has said.
Yvette Cooper called on the Home Office to launch their own investigation alongside police after allegations of sexual contact between guards and women kept at Yarl's Wood where made by a 23-year-old former inmate.
"A full and thorough investigation into these specific charges of abuse must be undertaken by the police and the Home Office immediately and testimony taken from all involved. This kind of alleged abuse is a serious criminal offence and should be treated as such.
"The Home Office needs to tell us whether and how long it has known of these allegations and what action it has taken to bring the police in."
An investigation has been launched after a former inmate of an immigration removal centre made allegations of inappropriate sexual behaviour against guards, police said.
A 23-year-old Roma woman claims she had sexual contact with male guards at Yarl's Wood in Bedfordshire, which her lawyer said could amount to misconduct in public office.
Harriet Wistrich of law firm Birnberg Peirce called on the Government to look at "what the hell is going on at Yarl's Wood" and raised concerns that this may not be the only case of sexual misconduct.
A Bedfordshire Police spokeswoman said: "We received a report at the end of August from a third party. No one has been arrested in connection with this investigation, but the investigation is ongoing."
Yarl's Wood has become the main removal centre for women in the UK and has been run by private security firm Serco since 2007.