A campaign to persuade investors to take their money out of the fossil fuel sector is growing faster than any previous divestment campaign and could cause significant damage to coal, oil and gas companies, according to a study from the University of Oxford.

The report compares the current fossil fuel divestment campaign, which has attracted 41 institutions since 2010, with those against tobacco, apartheid in South Africa, armaments, gambling and pornography. It concludes that the direct financial impact of such campaigns on share prices or the ability to raise funds is small but the reputational damage can still have major financial consequences.

"Stigmatisation poses a far-reaching threat to fossil fuel companies – any direct impacts of divestment pale in comparison," said Ben Caldecott, a research fellow at the University of Oxford's Smith School of Enterprise and the Environment, and an author of the report. "In every case we reviewed, divestment campaigns were successful in lobbying for restrictive legislation."

The report is part of a new research programme on stranded assets backed by Aviva Investors, HSBC, Standard & Poor's and others. It found: "The fossil fuel campaign has achieved a lot in the relatively short time since its inception."

Some major investors, such as the $74bn Scandinavian asset manager Storebrand, have already pulled their funds from coal stocks. But the researchers found that even if the maximum possible capital was divested by university endowments and public pension funds, the total was relatively small compared to the market capitalisation of traded fossil fuel companies and the size of state-owned enterprises.

However, the team concluded: "The outcome of the stigmatisation process, which the fossil fuel divestment campaign has now triggered, poses the most far-reaching threat to fossil fuel companies and the vast energy value chain."

Analysing previous campaigns, the researchers found examples of stigmatised companies being shunned by governments and being barred from public contracts or acquiring licences. "Stigma attached to merely one small area of a large company may threaten sales across the board," the report found, citing the examples of Motorola dumping its defence business due to bad press and Revlon's decision to disinvest from its South African operation after customer groups threatened a boycott.

The report also found instances when customers, suppliers and potential employees were scared off by stigma and where stigma had led shareholders to demand changes in the management of companies.

Bill McKibben, the environmental campaigner who leads the 350.org divestment campaign which is expanding from the US into Europe this autumn, said: "This divestment campaign is just one front in the climate fight, but of all the actions people can take to bring about structural change, it's probably the easiest. Severing our ties with the guys digging up the carbon won't bankrupt them--but it will start to politically bankrupt them, and make their job of dominating the planet's politics that much harder."

A report in April backed by climate economist Lord Stern found that at least two-thirds of the fossil fuels listed as assets by the world's fossil fuel companies would have to remain in the ground if governments were to fulfil their pledge of keeping climate change below the danger limit of 2C. The UN's Intergovernmental Panel on Climate Change (IPCC), backed by 193 governments, reached a similar conclusion at the end of September.

David Nussbaum, chief executive at WWF-UK, said: "With the IPCC giving us the clearest signal yet of the threats posed by a changing climate, it's clear that we must consider the risks to businesses and investors posed by investments in fossil fuels. Prudent investors want to be ahead of pack, not following the herd, so they will be preparing for a world where we leave fossil fuels in the ground."