In a leaked letter, Cameron said he wanted to mobilise businesses to look carefully at the risks of a leave vote.
"I am working with Peter Chadlington and Stuart Rose (the head of Britain Stronger in Europe) with a view to contacting FTSE 500 companies who have annual reports due for publication before June and persuading them that they should include Brexit in the list of key risks. All public companies are required to set out in their annual report an analysis of key risks," Cameron wrote.
Boris Johnson said the letter shows Downing Street was attempting to orchestrate a remain vote, even while publically claiming that it could campaign for an exit in the event of failing in its attempt to secure more protection for the UK in its relationship with the EU.
"This is the biggest stitch up since the Bayeux Tapestry. It stinks to high heaven. FTSE 100 chiefs are seeing their pay packets soar while uncontrolled immigration is forcing down wages for British workers," Johnson said.
"Now we learn that some fat cats have been secretly agreeing to campaign for remain while angling for lavish Government contracts. It makes us look like a banana republic. And it is also now beyond doubt that the so called renegotiation was a fiction designed to bamboozle the public. It was a meaningless mime, a ritual, a kabuki drama in which the outcome was utterly preordained. This is not the far-reaching and fundamental reform we were promised."
A spokeswoman for 10 Downing Street declined to comment.
However, speaking on behalf of the Remain campaign, Tessa Jowell, former secretary of state for culture, media and sport, said: “Boris Johnson used to have only praise for business leaders. The fact that he’s now shouting out conspiracy theories show the leave campaign are becoming desperate and losing the argument.
She added: “Great British employers overwhelmingly back remaining in Europe because it gives them free access to a market of 500 million – helping them to boost trade, create jobs, and cut prices.
It comes as the CBI has also found itself in the crosshairs of campaigners over a long-held stance that businesses should explain to their staff the risks of a Brexit vote.
The CBI estimates that roughly 80 per cent of its members support a remain vote.
CBI director-general Carolyn Fairbairn says: "Responsible business leaders should give their employees the choice to hear what impact a Brexit would have on company growth, their jobs and their local community.
"This is not about telling people how to vote but having calm, evidence-based conversations, whichever camp the business is in, or if they are neutral. And there are many different ways of engaging - whether it’s holding a ‘town hall’ style debate, setting up an internal information hub, or asking employees what questions they want answers to."
However, Vote Leave's business council chair John Longworth, who exited the British Chambers of Commerce in March over his own pro-Brexit views, said: "It’s highly regrettable to see big corporate bosses plotting to gang up on their staff, and lecture them on how to vote.
"The real question is the extent of the Prime Minister’s and Downing Street’s involvement in this. It is no secret that they have been coordinating with big business over the EU referendum - and working with the CBI to try to stifle debate, and intimidate the public into voting to remain in the EU.
"The referendum is an historic opportunity for the British people to decide on our future in the EU - and they are sick of seeing the establishment working to stitch up the contest and sell out Britain in favour of their own vested interests."