Ernest Hogg, 38, from Dundee, had been unconscious since he was brought by Group 4 officers to Hull Royal Infirmary on Tuesday. Prison officers said he had drunk 'hooch' - illegal alcohol brewed by prisoners.
He was found in the back of a Group 4 cell van, choking on his own vomit. The infirmary said inhalation of vomit led directly to fatal brain damage.
Yesterday Stephen Shaw, director of the Prison Reform Trust, described as 'catastrophic' Group 4's record since it was given the pounds 9.5m-a-year contract to run the Humberside and East Midlands prison escort service at the begining of April.
Last month, eight prisoners escaped from the company's custody, and Group 4 became a national laughing stock.
Mr Hogg's family said it was considering suing. Humberside detectives are investigating the death, and Group 4 has suspended six guards while the inquiry takes place.
Mr Hogg had been remanded in custody by Rotherham magistrates, charged with illegally importing cocaine. He was put in a Group 4 van returning him to the Wolds prison, Humberside - Britain's first private prison, which Group 4 also runs.
After dropping off two prisoners at Hull, Group 4 staff discovered that Mr Hogg was not well. They checked him and considered him fit to continue on the 50-mile journey. He was found on the floor of the van when staff got to the remand prison.
The Wolds was criticised in a Prison Reform Trust report last month which said that drug abuse and violence was commonplace. Judge Stephen Tumim, the Chief Inspector of Prisons, will investigate conditions in the private jail this month in what will be a politically charged inquiry. Ministerial approval for further jail privatisations may depend on his findings.
Derek Lewis, the commercial television executive whom Kenneth Clarke, the Home Secretary, brought in to be director of the prison service, supports giving prison management contracts to private companies.
Mr Shaw said: 'The Home Office is in a total panic. Group 4, the police and the prison service are all having investigations, and extra Civil Service monitors have been appointed to watch over the firm.
'This tragedy highlights the peculiar position Derek Lewis finds himself in. His press statements were widely perceived last month as giving strong support to the company.'
Tony Blair, the shadow home secretary, called for an urgent review and if necessary cancellation of Group 4 contracts. A Home Office spokesman said Mr Lewis was 'saddened to hear of the death of Mr Hogg'.Reuse content