A warning letter to key government ministers - signed by Jones and 17 big contracting firms - says Labour's public services programme will not be achievable without private contractors.
Unison has countered, saying privatisation is being introduced at the expense of decent pay and conditions for workers.
Unison general secretary Dave Prentis said:
'Digby Jones says the private sector isn't about driving down everybody's wages. Try telling that to the hospital cleaner who has just had her wages cut, or the school meals worker whose pension has just gone down the drain, or the home carer who has lost her holiday entitlement. Is it any wonder they are suspicious?
'Innovation by the private sector has been hard to find and efficiencies have been mostly at the expense of low paid women workers.
'Unison shares the government's objective of world class services, and it is our members in the public sector who will deliver those reforms.'
Unison wants newly recruited employees working for private contractors in the public sector to be paid the same as any workers transferred from the public sector.
But businesses want a voluntary code of conduct and promise to be exemplary employers, recruiting new staff on rates that are 'fair and reasonable'.
Unison's local government secretary Malcolm Wing urged DTLR minister Stephen Byers to intervene:
'We cannot go on negotiating indefinitely. We need some kind of outcome before the Labour local government conference in a fortnight.'
* Read about Digby Jones speech on LGCnet.