Britain is sleepwalking towards disaster because of a failure to recognise that climate change is causing the extreme weather that has blighted the country for more than a month, Ed Miliband has warned.

The Labour leader says in an interview with the Observer that climate change is now an issue of national security that has the potential not only to destabilise and cause conflict between regions of the world, but to destroy the homes, livelihoods and businesses of millions of British people.

Criticising David Cameron for appearing to backtrack on his commitment to the environmental cause, he calls on senior figures in all parties to unite behind the scientific evidence that climate change is a key factor in extreme weather. Failure to do so, he warns, will have catastrophic consequences.

Miliband says the science on the issue is now overwhelming, citing the government's own special representative on climate change, Sir David King, who recently warned: "Storms and severe weather conditions that we might have expected to occur once in 100 years in the past may now be happening more frequently and the reason is … that the climate is changing."

Miliband says: "In 2012 we had the second wettest winter on record and this winter is a one in 250-year event. If you keep throwing the dice and you keep getting sixes then the dice are loaded. Something is going on."

Suggesting the country rebuilds the frayed national consensus on climate change and shows the kind of cross-party unity seen in wartime, he adds: "We have always warned that climate change threatens national security because of the consequences for destabilisation of entire regions of the world, mass migration of millions of people and conflict over water or food supplies.

"But the events of the last few weeks have shown this is a national security issue in our own country too with people's homes, businesses and livelihoods coming under attack from extreme weather. And we know this will happen more in the future.

"The science is clear. The public know there is a problem. But, because of political division in Westminster, we are sleepwalking into a national security crisis on climate change. The terrible events of the last few weeks should serve as a wake-up call for us all."

With the Tory party divided over whether extreme weather can be linked to climate change, a leading independent adviser to the government has also joined the fightback against the sceptics. Lord Krebs, a member of the Climate Change Committee, described those who question the science as "the flat earthers of contemporary society who show a flagrant disregard for the future needs of our children and grandchildren".

Krebbs said not enough was being spent on flood defence because "we have not taken a long-term view of what needs to be done".

An Opinium/Observer poll shows more than half of voters (51%) believe the recent floods are a sign of climate change and global warming while 24% do not and 20% are neutral. Among young people aged 18-34, 60% blame climate change, while 44% of those aged over 55 take the same view. Some 51% say David Cameron has handled the crisis badly while 21% says he has done well.

Political fallout from the floods and storms continued as it was confirmed that three people died on Friday during weather which left tens of thousands of homes without power.

A woman killed in a car crushed by falling masonry in Holborn, Holborn, central London,, was named as minicab driver Julie Sillitoe, a 49-year-old mother of three. An 85-year-old man died after the 22,000-tonne liner Marco Polo, on which he was returning from a cruise to South America, was hit by a freak wave in the Channel causing water to enter through a window. The man was airlifted off the vessel with a woman in her 70s, but later died. Bob Thomas, 77, from Caernarfon, died in hospital after being hit by a falling tree in his garden on Wednesday.

More than 30 people had to be rescued from a seafront restaurant in Milford on Sea, Hampshire, after wind-blown shingle shattered windows and the sea flooded in.

Chief Inspector Gary Cooper, who co-ordinated the rescue, said it was probably the most difficult joint operation he had been involved in during his 28 years of policing. "The extreme weather conditions of stones being thrown from the beach with the power of the wind to smash windscreens of fire engines and military trucks was almost like they were being shot from a rifle," he said.

There was disruption across Britain's road and rail networks, with hundreds of trees uprooted. Many train services were cancelled. Some 22 severe flood warnings – indicating a danger to life – were issued for coastal communities from Cornwall to Hampshire, Gloucester and the Thames Valley, where rivers remain at their highest levels for decades.

Nearly 190 less serious flood warnings and 320 flood alerts were also in place on Saturday.

Miliband said he was ready to work with politicians of all parties, including "green" Tories such as Zac Goldsmith, to rebuild the consensus around climate change. He announced a three-point plan to tackle the crisis, including tougher decarbonisation targets, moves to strengthen the country's resilience to floods, and a push to boost business investment in the green economy.

He said that "dither and denial" would be disastrous for the country.