The Justice Secretary Chris Grayling had criticised the firms after it emerged that money had been claimed for tagging offenders who had already died.
Sadiq Khan said: “I have asked the Justice Secretary and he has declined to stop these two companies getting any further contracts, to delay the privatisation of probation until we know these two companies are clean.”
Speaking on Sky News the Shadow Justice Secretary implored the Government to reappraise services provided by G4S and Serco “across the piece”.
Earlier in the Commons the Justice Secretary announced he had asked the Serious Fraud Office to investigate G4S for overcharging for the tagging of criminals, including some who left the country or even died.
Chris Grayling said he was “angry” that contractors G4S and Serco had overcharged taxpayers by tens of millions of pounds.
The situation was a "wholly indefensible and unacceptable state of affairs”, the Justice Secretary told the House of Commons.
But he added: "At this moment of time I do not have evidence of dishonesty."
He also said that public safety had not been put at risk by the contractors' conduct.
The Howard League for Penal Reform said the Government should now rethink the role of private sector involvement in the criminal justice system.
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