In a letter to Prescott, the group plans to ask Labour to revive plans for a road and rail bridge west of Dartford Bridge, known as the Thames Gateway; a road tunnel at Blackwall; and a rail crossing at Woolwich. The three are worth a total of £600m.
British Airways chairman Sir Colin Marshall and Sir Allen Sheppard, former Grand Metropolitan chairman and head of lobby group London First, are among the signatories of the letter. The others are the leaders of Greenwich council and groups promoting development in south and east London.
Sources close to the lobbying effort described the letter as a plea to Prescott to give the go-ahead on projects ahead of the election of the London mayor in 2000.
They want planning and procurement work, likely to take 18 months, to start before the mayor is elected, even though the mayor would have to activate statutory procedures for the crossings.
To support their argument, London First and the London Development Partnership, chaired by Sir Colin, have commissioned research into the projects.
US investment bank Morgan Stanley has written a paper showing the possible corporate structure for a "bid vehicle" to build and run all three of the crossings.
In this, users of the new Blackwall tunnel and the road and rail Thames Gateway would pay a toll, with the money used to fund the Woolwich rail crossing.
Railtrack is envisaged as being part of the crossings construction group.
Transport consultant Maunsell has also carried out research to show what planning and statutory work is needed to allow the projects to go out to bid in 2001. This would enable work to start on site in 2003.
The business leaders want Prescott to provide public money to allow development work to start.
They were disappointed last year when Labour's transport white paper said that the London mayor would decide on the need for the new links, without committing further to the projects.
One source said: "We really want to see these projects happen. Business leaders can see the benefit of it – this is not an effort on behalf of, or by, contractors that simply want the building work involved in the crossings."