The world has a choice when dealing with climate change. One is to decide it's a problem like any other, which can be dealt with slowly and over time. The other is to recognise it as a crisis, perhaps the unique crisis in human history, which will take rapid, urgent action to overcome.

Science is in the second, scared camp – that's the meaning of the IPCC report issued last month, which showed that our planet is already undergoing climatic shifts far greater than any experienced in human civilisation, with far worse to come.

And those of us urging divestment from fossil fuel stocks are in the second camp too – we recognise that business as usual is quite simply impossible.

In fact, the most important feature of the IPCC report is probably that it adopted the analysis put forward by Carbon Tracker analysts in the UK and divestment activists who started their campaign a year ago in the US. The scientists' report quite explicitly said that most of the coal and oil and gas that the fossil fuel industry has identified and plans to mine or drill must remain in the ground to avoid climate catastrophe.

That in turn is why the fossil fuel industry, when it isn't in outright denial about climate change, falls into the first camp: slow, measured change would be nice. Because then we could pump up all the carbon we've told our shareholders and our banks about. Because then our stock prices will stay nice and high. Because then we won't have to confront reality – otherwise known as physics – for a while longer.

The gulf between these two camps poses a huge question for those who might think of themselves on the sidelines. Those, say, who own shares in the fossil fuel industry. In the US, a number of colleges, churches, and universities have begun to divest those stocks, arguing that they can't both simultaneously decry the wreckage of the climate and try to profit from it for a few more years.

The mayor of Seattle explained that his city was already spending millions building seawalls – what sense did it make to invest in the companies making that work necessary? The trustees of San Francisco State University recognised that it made no sense to have, on the one hand, a physics department understanding climate change and on the other hand, an endowment full of oil and gas stocks. The United Church of Christ, which traces its roots back to the Pilgrims, decided it couldn't pay the pastor by investing in companies that are running Genesis backwards.

This same opportunity is becoming part of a worldwide debate. From Africa come some of the loudest voices demanding divestment: Desmond Tutu, who watched the effectiveness of the movement a generation ago when it was stock in apartheid-tainted companies that was at issue, has asked us to take up the same tool. "If you could see the drought and famine in Africa, you would understand why," he says.

And it's not just North America responding. The Uniting Church in Australia, Anglican dioceses in New Zealand, and now the UK's Operation Noah have launched Bright Now – a church divestment campaign whose first success came earlier this month with the Quakers in Britain announcing they will disinvest from companies engaged in extracting fossil fuels making them the first UK Christian denomination to do so.

In addition, UK university students are increasingly engaged in divestment campaigns as evidenced by the work undertaken by People & Planet. To date there are 19 active divestment campaigns across the UK including universities with the largest endowments: Cambridge, Oxford and Edinburgh.

We'll be looking to grow the campaign this month with the Fossil Free Europe tour, a divestment road show with stops in Berlin, Amsterdam, Edinburgh, Birmingham and London.

Everyone involved in this campaign understands that divestment won't in fact bankrupt Exxon or BP or Shell, but they also understand how important it is to politically bankrupt them. These are now rogue industries, committed to burning more carbon than any government on earth thinks would be safe to burn. Their irresponsibility belongs to their executives and boards of directors – but it also belongs to anyone who holds their shares. If you think that climate change is a true crisis, then the time has come to sever your ties.