Human society faces a global health catastrophe if climate change is not effectively tackled at the UN conference in Copenhagen in December, leading doctors from around the world warn today.

Calling on medical practitioners everywhere to put pressure on politicians in advance of the meeting, the doctors say that the world's poorest people will be hit first by the health effects of global warming, but add that "no one will be spared".

Their stark challenge to governments follows a report in May which said climate change would represent "the biggest global health threat of the 21st century".

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Malaria, dengue fever and other tropical diseases would increase, the study predicted, spelling out how rising temperatures will cause health crises in half a dozen areas: there will be increased problems with food supplies, clean water and sanitation, especially in developing countries. Meanwhile, the migration of peoples will combine with extreme weather events such as hurricanes and severe floods to make for disastrous conditions in human settlements.

The doctors make their appeal as momentum begins to build for the UN conference, which will be held in the Danish capital from 7-18 December, and which will see the world community attempt to draw up a comprehensive new climate treaty to replace the 1997 Kyoto protocol. Its crucial objective will be drastic worldwide cuts in the emissions of industrial gases such as carbon dioxide which are causing the atmosphere to warm.

On Tuesday, the UN secretary general Ban Ki-moon is convening a climate change summit of world leaders in New York, including Gordon Brown and President Obama, to try to give some impetus to the tortuous pre-conference negotiating process – the draft text of 200 pages already contains 2,000 "square brackets": that is, points where the 190 countries taking part disagree.

The doctors' challenge to politicians to sort this out comes in a letter published simultaneously in Britain's two principal health journals, the British Medical Journal and The Lancet.

In the letter, Professor Ian Gilmore, the president of the Royal College of Physicians, joins 17 other national doctors' leaders from the US to Australia in saying: "There is a real danger that politicians [at Copenhagen] will be indecisive, especially in such turbulent economic times as these. Should their response be weak, the results for international health could be catastrophic."

They go on: "Doctors are still seen as respected and independent, largely trusted by their patients and the societies in which they practise ... As leaders of physicians across many countries, we call on doctors to demand that their politicians listen to the clear facts that have been identified in relation to climate change and act now to implement strategies that will benefit the health of communities worldwide."

The letter follows the report on the health effects of global warming which was launched jointly last May by The Lancet and University College London (UCL), and which squarely labelled climate change as the 21st century's biggest global health threat.

That report's lead author, Professor Anthony Costello, director of UCL's Institute for Global Health, said at the time: "The big message of this report is that climate change is a health issue affecting billions of people, not just an environmental issue about polar bears and deforestation. The impacts will be felt not just in the UK, but all around the world – and not just in some distant future but in our lifetimes and those of our children."

Today's letter is accompanied by an editorial written by two of Britain's most senior figures in the area of health and development: Professor Sir Michael Marmot, director of the UCL International Institute for Society and Health, and Lord Jay of Ewelme, who as Sir Michael Jay was head of the Foreign and Commonwealth Office, and is now chair of Merlin, (Medical Emergency Relief, International), the UK charity which provides healthcare and medical relief for vulnerable people caught up in natural disasters, conflicts and major disease outbreaks.

The two men write: "A successful outcome at the UN climate change conference in Copenhagen this December is vital for our future as a species, and for our civilisation." And they echo the writers of the letter in asserting: "Failure to agree radical reductions in emissions would spell a global health catastrophe."

They point out that there is now wide consensus that global temperatures are rising and that human actions are responsible; that there is a need to cut carbon emissions by at least 50 per cent of 1990 levels by 2050 to avoid dangerous climate change; and that the economic argument that taking action now rather than later will be cheaper has also been widely accepted since the Stern report in 2006. Furthermore, they say, the election of President Obama has shifted policy in the US from seeking to block an agreement to seeking to find one.

They go on: "So the chances of success should be good but the politics are tough. The most vocal arguments are about equity: the rich world caused the problem so why should the poor world pay to put it right? Can the rich world do enough through its own actions and through its financial and technological support for the poor to persuade the poor to join in a global agreement?"