“I should state that I have no information to confirm that dishonesty has taken place on the part of either supplier,” he added.
“But given the nature of the findings of the audit work that has taken place so far, and the very clear legal advice that I have received, I am today asking the Serious Fraud Office to consider whether an investigation is appropriate into what happened in G4S.”
But G4S sources stressed no evidence of dishonesty had been discovered by either the MoJ review or its own inquiry carried out with the assistance of external experts.
They said the firm had co-operated fully with the MoJ and was given the choice of another audit by management consultants or a referral to the SFO.
G4S had preferred calling in the SFO, they added, to investigate any claims of dishonesty.
They insisted that they had found “absolutely no indication” that it had not complied with the terms of its contract.
But shadow justice secretary Sadiq Khan was stunned by the allegations.
“To the public this appears a straightforward fraud - obtaining property by deception,” he said.
Keith Vaz, Labour chairman of the Commons home affairs committee, added: “G4S should never have got another Government contract after the shambles of the Olympics.”
Cabinet Office minister Francis Maude announced a government-wide review of contracts held by G4S and Serco.
Serco Group, which runs the Boris Bike scheme, said it would repay any amount agreed to be due and that given the investigation, it had decided to withdraw from the re-tendering process for the electronic monitoring service.
The company’s chief executive Christopher Hyman said: “We will not tolerate poor practice and behaviour and wherever it is found we will put it right.”