To cries of "rubbish" from delegates at the Prison Officers' Association annual conference in Portsmouth, Mr Straw said that Home Office research had shown that private firms would not agree to build jails that they could not manage themselves.
Mr Straw walked into the conference hall to be greeted by stony silence as he attempted to strike up a new partnership of conciliation with prison officers furious that he has not restored their trade union rights.
But the prospects for peace were dealt a crippling blow by what union leaders described as a "bombshell" disclosure by the Home Secretary.
Mark Healy, chairman of the POA, said: "This means that every jail that's going to be built in the future is not only going to be built with private money but run by private firms."
He claimed that because private jails were cheaper to run and had fewer staff, the development would have implications for public safety and would mean that prisoners were less likely to receive rehabilitative treatment.
But the Home Secretary said that he had become a convert to the idea of privately run jails and he could not ignore a succession of independent reports which had paid tribute to their efficiency and value for money.
Mr Straw said that a Home Office review had found that private companies were not prepared to accept the risk of investing in the building, design and maintenance of a jail while allowing the public sector to manage the establishment. He said: "I must conclude that there is no way that such a proposition is affordable and it certainly does not offer value for money."
The Home Secretary said that the public sector would be allowed to bid for future control of privately run jails when their management contracts ran out, but union leaders said the prison service had no realistic prospect of success.
Because no new publicly run prisons have been built since 1992, Mr Straw's announcement makes it unlikely that any new jails would be run directly by the prison service, said Mr Healy.
Mr Straw's brave decision to address what was always likely to be a hostile audience made him the first Home Secretary to attend the POA's annual conference in recent years.
A succession of delegates queued up to denounce him variously as a "liar" and "the right dishonourable Mr Straw", accusing him of reneging on promises to restore full trade union rights to the POA.
In an effort to build a "constructive partnership", Mr Straw yesterday offered to revoke the legislation introduced by his predecessor Michael Howard, making it a criminal offence for a prison officer to take industrial action. He said he wished to introduce instead a new civil law which would prevent such action.
Mr Straw wants prison officers to have the same union rights as police officers and staff at GCHQ who are prevented from taking industrial action but have recourse to an independent body which reviews pay and conditions.
After an emergency motion, the union agreed to enter into negotiations with the Home Secretary.Reuse content