The decision to pull out of the bidding leaves Bouygues to battle it out with French rival Vinci, in joint venture with regeneration specialist St Modwen, for the £1bn Vauxhall scheme.
Nigel Durman of Drivers Jonas Deloitte, which is handling the sale, said: “CGMA have been informed by Barratt Developments and Kier Group that they have chosen not to continue in the tender process for The Garden at New Covent Garden Market and we respect their decision.
“This is an inevitable part of the competitive dialogue process as we seek to reduce an initial short-list of six down to a single preferred development partner.”
He added: “We continue to have strong dialogue with both Bouygues UK and Vinci/St. Modwen Properties for what is a hugely exciting development opportunity.”
The 57 acre site, in Vauxhall, South London, will be redeveloped at no cost to tax payers to provide a new modern market, 2,300 apartments, a hotel, shops, a major grocery store and community facilities including a food industry training suite.
But the complexity of the scheme and phasing is understood to have concerned the Barratt/Kier consortium.
Under the present plan, the winning consortium will be expected to build a £100m new market before it can move onto phased house building at the huge site.
The landmark London scheme was highlighted yesterday in housing minister Grant Shapps great public land disposal plans as an example of Government action to sell on land for housing.
New Covent Garden Market is part of the Nine Elms Opportunity area, which includes Battersea Power Station and the future home of the American Embassy.
The two remaining consortia are due to submit their final bids for the project this month.