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The list is held by Nirex, the government-controlled agency charged with finding a long-term repository for the waste which will remain deadly for millions of years.
It was drawn up in 1989 but ministers refused to publish it for fear of local protests and of blighting property values in each area.
Two favourite sites, at the Sellafield nuclear plant in Cumbria and the Dounreay plant in Caithness, were made public but the rest were not.
Nirex wants to disclose all the sites as part of a public debate on where Britain’s waste should now be dumped. They are understood to include an RAF base at Thetford in Norfolk and a site managed by the United Kingdom Atomic Energy Authority (UKAEA) at Harwell in Oxfordshire.
Others include two uninhabited islands off the west coast of Scotland and two further sites in the seabed. There was also a proposal to build an artificial island off Scotland.
Nirex, which was established in the 1980s to oversee the storage of radioactive waste, has written to local authorities and environmental groups to arrange a meeting on May 26 at the Thistle Manchester hotel.
Chris Murray, managing director of Nirex, said: “These sites were based on a sound technical study. Some of them we could now rule out, but we could still be interested in others. The key point is that the next debate over where any repository is sited must be a public one and not secret.”
Nirex wants to avoid a repeat of the public protests and humiliation that it suffered the last time it tried to build an underground facility. Its proposal for an experimental “rock characterisation facility” under Sellafield was rejected by John Gummer, then environment secretary, after a public inquiry showed that the project had been shrouded in confusion and secrecy.
Murray wants to follow the example set by Finland and France which held public consultations on where to site their nuclear repositories. Britain could also follow the French example by offering inducements such as schools and leisure centres to communities close to the facility.
Plans to publish the list come as the government confirmed this weekend that Britain could build a new generation of nuclear power plants to help to combat climate change. Alan Johnson, the new productivity, energy and industry secretary, said it would re-examine the question “some time this year”.
Britain’s 14 reactors produce a quarter of the nation’s electricity, but because of their age all but one will have to close by 2023.
For supporters of new nuclear power stations, one of the biggest problems is that Britain still has no means to dispose of radioactive waste. A government committee is expected to recommend an underground repository but will not report until late next year. If agreement were reached and a dump were built it would become much easier to argue the technical case for more power stations.
The 12 sites were identified after work by the British Geological Survey. They were extracted from a longer list of about 500 sites that were geologically suitable including parts of the home counties, Leicestershire, Yorkshire and Cheshire.
Many inside the nuclear industry are known still to favour Sellafield as the best place for an underground dump, largely because this would avoid transporting a lot of waste around the country.
There is likely to be intense local opposition. Martin Forwood, campaign director at Cumbrians Opposed to a Radioactive Environment, said that the area’s geology was unsuitable: “If they think they are going to saddle us with the country's nuclear dump they are going to have a God-almighty battle on their hands.”
The pro-nuclear lobby received a setback last week when it emerged that the Thorp reprocessing plant at Sellafield had suffered a big radioactive leak. A burst pipe allowed the escape of about 100 tons of highly corrosive nitric acid containing 20 tons of dissolved uranium and plutonium. Insiders admitted that workers had not spotted the leak, which had gushed waste for weeks.
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