They said they were confident that such a review would exonerate the government and insisted that deputy prime minister John Prescott should go ahead with the part-privatisation.
The threat of a judicial review, initiated by the Greater London Authority and its transport chief Bob Kiley, comes as the rift between the bidders, the government and the GLA over the public-private partnership deepens.
The government this week vowed to press on with the PPP in defiance of GLA opposition, which is based largely on safety fears after the the Hatfield train crash.
One bidder said the scheme would go ahead and dismissed criticisms from Kiley, the Transport for London commissioner, that the PPP bids were ill thought out.
The bidder said: "We think any judge will be satisfied that the bids meet the needs of ensuring a safe and efficient system.
"When a judge sees the level of detail submitted in the bids I think the government will win. We are not seriously concerned to the point of break-up." The decision to opt for a judicial review follows the breakdown in talks between Prescott and Kiley, after months of negotiations.
Other bidders reacted with fury to Kiley's claims that the PPP bids were too expensive and too vague. One bidder said: "That is just nonsense. We have detailed project scopes, prescribed improvements that have to be made and savings identified.
"The bidders cannot understand how he can make these comments. I find it quite extraordinary that he can say that." Another bidder said: "We have spent the last 14 months on the bids – there are 15 boxes of documents and 100 people working on this. I wonder what people think we have been doing all this time." The parting of the ways between the GLA and the government came despite the DETR's offer to Kiley last week of an auditing role over the maintenance of the Tube infrastructure.
Kiley claimed that the government refused to agree to his proposal that unified management control be given to Transport for London.