More than half of those affected by the recent flooding were not satisfied by how the coalition reacted to the crisis.
According to a poll of 1,000 people living in Oxfordshire, West London, Somerset and Cornwall, three out of five were unhappy by how the Government responded to the severe weather.
More than one in five of those questioned for the Climate Coalition said they were more worried about climate change following the emergency.
The research was published ahead of a meeting in Brussels by European leaders in a bid to negotiate a new set of targets on climate and energy for 2030.
Greenpeace UK executive director John Sauven said: "These floods show beyond doubt that Britain can't pull up a drawbridge to keep itself safe from the risks of climate change.
"It's time our government got serious about pushing for real action across the UK and Europe to slash the polluting emissions that are driving more extreme weather.
"The EU summit is David Cameron's first test to prove he's learned the lessons from the floods and is taking climate security seriously.
"There's a whole new constituency of people, including many in Cameron's own county, who have experienced the brutal force of flooding for the first time.
"How he responds to the risks of climate change is becoming a major political issue which the Prime Minister will duck at his peril."
Oxfam campaigns and policy director Ben Phillips said: "The recent extreme weather in the UK offered us all a glimpse of what climate change could mean for us in the future.
"Around the world, poorer people are already feeling the effects of climate change with increasingly unpredictable and extreme weather disrupting seasons and hampering food production.
"David Cameron should push the EU to be more ambitious in cutting emissions to protect people in the UK and overseas from climate change."
Campaigners staged a demonstration in Westminster, parading a replica of a waterlogged 10 Downing Street.