The first study to combine computer models of rising temperatures with records of the ancient climate has indicated that sea levels could rise by up to 20ft (6m) by 2100, placing millions of people at risk.

The threat comes from melting ice sheets in Greenland and Antarctica, which scientists behind the research now believe are on track to release vast volumes of water significantly more quickly than older models have predicted. Their analysis of events between 129,000 and 116,000 years ago, when the Arctic last warmed to temperatures forecast for 2100, shows that there could be large rises in sea level.

While the Greenland ice sheet is expected to start melting as summer temperatures in the Arctic rise by 3C degrees to 5C (5.4F-9F), most models suggest that the ice sheets of Antarctica will remain more stable.

The historical data, however, show that the last time that Greenland became this warm, the sea level rise generated by meltwater destabilised the Antarctic ice, leading to a much higher increase than can be explained by Arctic ice alone.

That means that the models of sea-level rise used to predict an increase of up to 3ft by 2100 may have significantly underestimated its ultimate extent, which could be as great as 20ft.

Such a rise would threaten cities such as London, New York, Bombay and Tokyo. Large parts of the Netherlands, Bangladesh and Florida would be inundated, and even smaller rises would flood extreme low-lying areas, such as several Pacific islands and New Orleans.

“Although the focus of our work is polar, the implications are global,” said Bette Otto-Bliesner, of the US National Centre for Atmospheric Research in Boulder, Colorado, who led the study. “These ice sheets melted before and sea levels rose. The warmth needed isn’t that much above present conditions.”

Her colleague, Jonathan Overpeck, of the University of Arizona, said: “This is a real eye-opener set of results. The last time the Arctic was significantly warmer than the present day, the Greenland ice sheet melted back the equivalent of two to three metres (6ft-10ft) of sea level. Contrary to what was previously believed, the research suggests the Antarctic ice sheet also melted substantially, contributing another 6ft to 10ft of sea level rise.”

The findings, which are published today in the journal Science, have emerged from a study that used data from ancient coral reefs, ice cores and other natural records to reconstruct the climate during the last gap between Ice Ages. In this interglacial period, between 129,000 and 116,000 years ago, temperatures in the Arctic were between 3C and 5C above present levels — a similar level to that predicted for the end of this century.

The scientists found that meltwater from Greenland raised the sea level by up to 11ft, but coral records showed that the total global rise was between 13ft and 20ft. Dr Overpeck said that the melting of Antarctic ice sheets was the most likely explanation. As sea levels rose, the floating ice shelves off the coast of the continent would have become more likely to break up. That in turn would have allowed glaciers to dump more ice from the continent itself into the sea.

He said that this was particularly worrying at present as the base of the West Antarctic ice sheet lay below sea level, which would allow ice to escape to the sea easily.

Several recent studies have indicated that the Greenland ice sheet, which contains enough water to raise sea levels by 23ft, and the West Antarctic sheet, which holds enough for a 20ft rise, are thinning. Both are expected to take several centuries to melt completely, but could release substantial quantities of water by 2100.

Dr Overpeck said that the results added to the urgency of measures to control the greenhouse gas emissions contributing to global warming.