Richard Branson has failed to deliver on his much-vaunted pledge to spend $3bn (£1.8bn) over a decade to develop a low carbon fuel.

Seven years into the pledge, Branson has paid out only a small fraction of the promised money – “well under $300m” – according to a new book by the writer and activist, Naomi Klein.

The British entrepreneur famously promised to divert a share of the profits from his Virgin airlines empire to find a cleaner fuel, after a 2006 private meeting with Al Gore.

Branson went on to found a $25m Earth prize for a technology that could safely suck 1bn tons of carbon a year from the atmosphere. In 2009, he set up the Carbon War Room, an NGO which works on business solutions for climate change.

But by Klein’s estimate, Branson’s “firm commitment” of $3bn failed to materialise.

“So the sceptics might be right: Branson’s various climate adventures may indeed prove to have all been a spectacle, a Virgin production, with everyone’s favourite bearded billionaire playing the part of planetary saviour to build his brand, land on late night TV, fend off regulators, and feel good about doing bad,” Klein writes in This Changes Everything, Capitalism vs The Climate.

Klein uses Branson and other so-called green billionaires – such as the former New York mayor, Michael Bloomberg – as case studies for her argument that it is unrealistic to rely on business to find solutions to climate change.

Branson routed a first pay-out of his $3bn commitment, about $130m, through a new Virgin investment company into corn ethanol.

The fuel has now been widely discredited as a greener alternative to fossil fuels, because of its climate change impacts and for driving up the cost of food.

Virgin went on to look at other biofuels, at one point exploring a project to develop jet fuel from eucalyptus trees. “But the rest of its investments are a grab bag of vaguely green-hued projects, from water desalination to energy efficient lighting, to an in-car monitoring system to help drivers conserve gas,” Klein writes.

By last year, the total of those investments, in corn ethanol and elsewhere, amounted to about $230m, she estimates. Branson made an additional small investment in an algae fuel company, Solazyme. But Branson still puts the total spend at well under $300m – just a tenth of his $3bn pledge.

The British entrepreneur has acknowledged that his efforts to mobilise large investments on cleaner fuels have fallen short. However, he told the Observer earlier this year he had lost many millions in failed green investments.

“There is no question that Virgin is involved in a number of businesses that emit a lot of carbon, and that is one of the reasons why I have to work particularly hard … but, more importantly, to try to help other people balance their books as well,” he said.

“We have invested hundreds of millions in clean technology projects. We haven’t made hundreds of millions profit,” he said.

Branson also told the Observer that he felt he had a responsibility to do something for the climate – given that so much of his empire is built on carbon-intensive transport industries.

“There is no question that Virgin is involved in a number of businesses that emit a lot of carbon, and that is one of the reasons why I have to work particularly hard … but, more importantly, to try to help other people balance their books as well,” he said.