Recent fraught debates around the energy bill saw coalition MPs – including some climate-sceptic Conservatives – oppose a target for making electricity carbon-free by 2030. But this was only the latest reason to suspect that David Cameron's 2010 promise to lead the "greenest government ever" was simply post-electoral exuberance.

From widespread backbench opposition to the siting of windfarms, to a dash-for-gas strategy endorsed by the Treasury (but criticised by the government's own Committee on Climate Change), Conservative rhetoric on climate change and the environment has undergone a drastic shift.

While opposition to windfarms does not necessarily entail climate change denial, the signals from the government are worrying. It is well known that Conservative voters are more likely to be sceptical about climate change. And with no indication from political leaders on the right that climate change is a problem that their voters should care about, there is a risk that the cross-party consensus on climate change in the UK could begin to unravel.

If the centre-right does not develop an effective and coherent narrative on climate change, then everyone has a problem. The challenge for communicators of all political stripes is to identify the ideas that will fire the imagination of citizens with centre-right views more effectively than the seductive, do-nothing arguments of sceptic groups like the Global Warming Policy Foundation.

In a new report for the Climate Outreach & Information Network (Coin), launched on Thursday, we argue that there is no inherent reason why climate change and the values of centre-right should be incompatible. However, there is a vacuum where a compelling conservative narrative on climate change should be – something which the report, entitled A new conversation with the centre-right about climate change, takes the first steps towards addressing.

The report is a response to a meeting Coin convened with some of the UK's leading experts on conservative engagement with climate change. We asked them to identify the key barriers and opportunities for more effectively communicating about climate change with this audience. In the words of one meeting participant, climate change must "break out of its leftwing ghetto" in order for a meaningful new conversation with the centre-right to begin.

We then conducted a thorough review of the research evidence, summarising key principles for climate change communication and identifying four narratives for talking to the centre-right about climate change.

The first narrative we labelled "localism", drawing on recent work by the conservative philosopher Roger Scruton. A core part of the British centre-right philosophy is a love of our "green and pleasant land". Stewardship, trusteeship and a shared responsibility to protect it are all embedded deeply at the heart of conservatism. Climate change poses new dangers to the countryside – and so should be something that conservatives want to address.

The second narrative focuses on energy security, and the idea that decarbonising is a sensible, cautious – conservative – strategy for insuring ourselves against energy risks in the future. The third narrative draws on work by the journalist James Murray, whose vision of "new environmentalism" positions climate change as too important for hippies and lefties, and argues that the innovators, decision-makers and businesses should be leading on climate change.

The final narrative we call the "good life". Emerging research suggests that framing climate change as a health threat may be a good way of reaching people who see climate change as something that only environmentalists need to worry about. And for conservatives who care about the health and wellbeing of their local communities, this may be a better way to start a conversation about climate change.

The aim of the report is not to advocate for particular policies, or to accuse people with centre-right views of being irrational, misguided or somehow wrong in how they think about climate change. Too many analyses of climate change scepticism assume that throwing more facts at the debate will somehow convince sceptics to change their minds; that the problem is simply a lack of knowledge about climate science.

But we know from academic research that what determines perceptions of climate change is not only – not even mostly – people's knowledge about the science. It is their values and political views that more directly influence their attitudes about climate change and how to respond to it.

So our report is an attempt to turn the debate about climate change scepticism upside down. Instead of asking how we can convince climate sceptics on the right that they are wrong, why not start a new conversation about why people with centre-right views should care about climate change, and what a centre-right solution to climate change would be?

• Adam Corner leads the Talking Climate programme for the Climate Outreach & Information Network. The report was funded by the BRASS research centre at Cardiff University.