The shareholder revolt at oil giant ExxonMobil over its climate change policy and corporate governance practices gathered fresh momentum today after four UK institutional investors signalled their support for one of the shareholder resolutions proposed earlier this month by the billionaire Rockefeller family.

In a move industry watchers said underlined the growing pressure from investors for firms to develop extensive climate change strategies, F&C Asset Management, Morley Fund Management, the Co-Operative Insurance Society and the West Midlands Pension Fund are throwing behind the resolution demanding that ExxonMobil appoints an independent chairman.

Currently, Exxon's chief executive Rex Tillerson also holds the position of chairman, a practice that while not uncommon is widely regarded as being in contradiction to corporate governance best practices.

The resolution - proposed by leading shareholders within the Rockefeller family, whose ancestor oil tycoon John D Rockefeller founded the original business – forms part of a package of four separate resolutions all designed to stimulate greater debate on the company's board and instigate a reversal of its hardline approach on global warming and relatively limited investment in renewable energy.

Speaking at the launch of the resolutions earlier this month, economist Neva Rockefeller Goodwin said that the company was guilty of ignoring both the scale of the business risks posed by climate change and repeated attempts by shareholders to discuss the issue.

"There are an awful lot of people who are getting increasingly annoyed with Exxon," she observed, adding that some of the company's billions "should go towards looking to the future and to the kind of energy this world might need".

Exxon has been repeatedly criticised by environmentalists in recent years for its failure to engage with climate change issues to the same extent as many of its rivals in the oil industry.

The company has repeatedly claimed that renewable energy remains economically unviable, but critics argue that it is failing to prepare for legislative and economic environment in which demand for clean energy will increase. While rivals such as BP and Shell have invested billions of dollars in beginning to diversify their energy mix, Exxon's climate change efforts centre on a relatively modest $100m commitment to fund a Stanford University project on climate change and a recent announcement to trial carbon capture and storage technologies.

Speaking to The Guardian newspaper, F&C Asset Management's director of governance and sustainable investment, Kevin Litvack, said that the appointment of a separate chairman could help prompt a rethink over the firm's environmental policies.

"Despite top-notch individual directors, the company's record over the last decade, particularly regarding climate change, demonstrates that debate has been lacking," he said. "By bringing in an independent chairman, the company can better leverage that creativity and challenge, and avoid over-dominance by management."

Paul Simpson, chief operating officer of the Carbon Disclosure Project, a lobby group committed to promoting wider corporate reporting of environmental impacts, said the move highlighted the extent to which some shareholders are now willing to go to in order to ensure the firms they invest in have a responsible approach to tackling climate change.

"There has been a lot of quiet conversations between Exxon and some of its leading shareholders for quite some time, but the fact that the Rockefeller's have gone public with these resolutions is a watershed moment," he said. "It shows how serious many large investors are taking climate change issues."

He added that should the resolutions gain enough support then Exxon would be obliged to respond, but even if they are rejected significant damage has already been done to the firm's brand. "It happens very rarely, but ultimately shareholders have the capacity to get rid of the board and you can't afford to ignore them," he said. "We are going to see more and more of these types of shareholder revolts at companies that are either seen as laggards on climate change or are regarded as not matching the efforts of their peers."