BP declined to comment on the campaign.
The investor group can't be certain whether its efforts played into BP's decision to reduce the value of its assets by up to $17.5 billion, announced on June 15.
But they have already begun lobbying building materials company CRH and plan to write to Anglo-Australian miner Rio Tinto, which supplies the steel industry. Along with cement, steel is a major source of greenhouse gases.
"We will be rolling out similar engagements with other fossil fuel-dependent companies," Landell-Mills, who is coordinating the campaign, told Reuters in an interview.
The investors were also planning to include European and U.S. banks financing fossil fuel projects, Landell-Mills added.
Rio Tinto and CRH declined to comment.
Early last year, the investors began lobbying the Big Four accounting firms - EY, Deloitte, PwC and KPMG - to do more to ensure climate-related risks are adequately reflected in company financial statements they audit.
The campaign is one of a number of efforts by investors to push companies on environmental policies, amid concerns many businesses are both contributing to the planet's warming while also failing to take full stock of the risks they face.
Major fund managers including BlackRock have issued increasingly strident public statements about climate change, while other investors have threatened to pull money out of Brazil unless Amazon deforestation is curbed.
The campaign led by Sarasin & Partners emphasizes the legal duty companies have to ensure their financial statements fully reflect how government moves to ratchet up climate action and the falling costs of renewable energy are likely to affect future profitability.
"It's a very serious thing from their perspective," said Landell-Mills. "This is a matter of ensuring there is no misrepresentation going on."
Accounting for potential future losses can weaken a company's balance sheet, making it harder to finance new investment in carbon-intensive activities such as oil exploration, the investors argue.
The coalition includes Sarasin & Partners, M&G Investments, Jupiter Asset Management, NN Investment Partners and pension funds such as the Brunel Pension Partnership and Denmark's PKA.
Although it was difficult to independently assess the impact of the campaign, Landell-Mills pointed to a series of moves that align with the investors' demands in letters sent to BP, Anglo-Dutch major Shell and France's Total in November.
In the letters, seen by Reuters, the investors questioned whether the companies' oil price assumptions, which form the bedrock of their accounts, were aligned with the 2015 Paris climate accord, which implies sharp cuts in fossil fuel use.
Before BP's writedown, the group's letter to the British oil major said: "We have concerns that, at present, BP's accounts may be overlooking material climate considerations, and consequently potentially overstating both performance and capital." The same language was used with Shell and Total.
Total did not immediately respond to a request for a comment. Shell said it had "comprehensively responded" to similar demands by the investor group, and included climate risks in its accounts.
"Since that time, Shell has also published an ambition to be a net zero energy company by 2050, or sooner," Shell said in an email to Reuters on Sunday.
Last week, BP cut its benchmark Brent oil price forecasts to an average of $55 a barrel until 2050, from $70, saying it expects a collapse in oil demand during the coronavirus pandemic to accelerate a low-carbon transition.
BP also said it would have to review some plans for early stage oil and gas exploration projects.
Meanwhile, Shell also lowered its long-term Brent crude expectations to $60 a barrel, from the 2018 price of $70, in its 2019 annual report published in March. Total also reduced its price assumptions at about the same time.
While majors often adjust price assumptions, the investors noted that Shell's auditor's report contained substantially more references to climate risks than the previous year.
"It's tip of the iceberg," Landell-Mills said. "And investors will have to understand that they (oil majors) are not going to be able to pay dividends like they did before." ($1 = 0.8102 pounds)
(Reporting by Matthew Green Simon Jessop; Additional reporting by Zandi Shabalala in London; Editing by Katy Daigle and Lincoln Feast) ((email@example.com; +44 (0) 207 542 5052; Reuters Messaging: Reuters Messaging: firstname.lastname@example.org))