But much of the support comes with reservations, making it crucial for the government and energy companies to engage local communities, according to a survey presented to Britain's Royal Society.
This requires more than the traditional "decide and defend" approach to choosing new locations, said Nick Pidgeon, a psychologist at Cardiff University and Peter Simmons of the University of East Anglia in Norwich, who led the survey.
"The views of people living in these areas is quite complicated and it isn't as simple as 'for' or 'against,' Simmons told a news conference. "The way this is done is going to be very important."
The results of the five-year study follow French utility EDF's 12.5 billion pound ($22.5 billion) agreed bid for British Energy, which operates Britain's eight nuclear power stations.
The British government gave the green light to nuclear power stations earlier this year, saying they would help meet climate change targets and reduce dependence on imported energy and dwindling North Sea oil and gas supplies.
The eight existing British Energy plants all have ready-made infrastructure and ample space around them to make promising sites for next-generation facilities.
"It is becoming clear... that initial proposals for new nuclear build will include existing nuclear sites," the researchers said in their report.
The five-year survey included residents of three communities living within 10 miles of three nuclear plants in Britain, a number of whom knew people working in the facilities.
About a third of residents said they believed the plants were safe and reported trust in local operators to keep the plants safe. Another nearly 40 percent viewed nuclear power as risky but accepted it as a way to address climate change and energy security needs.
A further 12 percent said their was no point worrying while 16 percent of respondents said the risks of nuclear power far outweighed any benefits. These people also had little faith in the nuclear industry and government.
The researchers also noted that communities without nuclear plants usually put up fierce opposition to proposals for such facilities, making it logical the government will seek existing locations.
But while people living near nuclear plants overwhelmingly supported the idea of new facilities, the fact that a significant number of them only offered qualified backing means the government could easily run into roadblocks.
"Nearly 40 percent were expressing conditional support, which is much more vulnerable to change," Simmons said. "The way these (decisions) are conducted is going to be very important.