The Home Office is drawing up plans to scale up a G4S-run immigration contract despite a government-wide freeze on new dealings with the company while it is being investigated for allegedly defrauding the Ministry of Justice.

According to information obtained by the Guardian, the private security firm is preparing to expand capacity by 30% at one of the two immigration removal centres it runs on behalf of the Home Office, even though it is facing a formal investigation by the Serious Fraud Office for claims it overcharged the government in electronic tagging contracts.

Labour said it was bizarre and wrong that the company was being rewarded with bigger contracts while it was under investigation.

Brook House removal centre, near Gatwick, holds people due for deportation from the UK, and currently has space for 426 male detainees. Last month, while hosting a reception for outside contractors, the centre's director, Ben Saunders, said the company intended to increase this by 60 and then another 70 places over "the earliest possible timeframe".

On Monday, the Serious Fraud Office launched a formal criminal investigation into G4S after the justice minister, Chris Grayling, revealed in the summer that its staff had been billing the Ministry of Justice for tracking the movements of offenders who had gone abroad, been returned to jail or even died.

Grayling promised that G4S would not be awarded any new contracts by his department until investigations into G4S billing practices had been completed.

The Cabinet Office confirmed this pledge was binding across all government departments and was itself auditing several other G4S contracts.

Grayling said he had no direct evidence of dishonesty. G4S said its internal investigation had found no evidence of fraud and the security multinational was co-operating with the SFO investigation.

Last month, the head of UK and Irish operations for G4S , Richard Morris, resigned in a move understood to help patch relations between the company and the government.