A list of 12 sites considered for storing nuclear waste in the 1980s and 1990s has been released under the Freedom of Information Act.
Many believe a storage site at Sellafield is the most likely option
The list included uninhabited Hebridean islands Fuday and Sandray, and offshore sites near Hunterston and Redcar.
Other sites were in Essex - at Bradwell and near Southend - Stanford, in Norfolk, and at Sellafield and Dounreay nuclear power stations.
The body handling waste says any future sites will be chosen from scratch.
The list was released by Nirex, which is responsible for dealing with Britain's intermediate-level nuclear waste.
It was drawn up in the 1980s, but the plan to bury waste at the sites was abandoned following the landslide defeat of Mr Major's Conservative government in 1997.
Waste is currently stored at more than 30 sites around the country.
Potton Island, Essex
Two sites at Sellafield, Cumbria
Killingholme, South Humberside
Offshore site near Redcar
Offshore site near Hunterston
Nirex is emphasising that the released list is purely historical and when a decision is made on where to store nuclear waste, the list would not become the starting point of a new exercise.
The issue is sensitive with some energy experts beginning to say that Britain can meet pollution targets only if it builds a new generation of nuclear plants.
One of the sites considered was in Essex, at the former Ministry of Defence facility at Potton island, just a few kilometres from the centre of Southend. Another was at the former nuclear power station at Bradwell.
Sellafield remains a favourite, with much nuclear material already there, and the local population seen to be supportive. Two sites at the Cumbrian plant are on the list.
A site at Dounreay nuclear power station presented another while in Caithness, a site at Altnabreac was discussed.
There has been speculation about Stanford in Norfolk, where the MoD owns land, which is also on the 1980s list.
The current government is looking for a definite solution to nuclear waste storage, and will start from scratch.
Its Committee on Radioactive Waste Management will report next year but will only give technical specifications, such as whether nuclear waste will be below or above ground and how it will be monitored.
Site selection will follow later. The offshore sites are understood not to be an option now because of changes in the law.
Chris Murray, managing director of Nirex, said: "Radioactive waste exists and needs to be dealt with whether or not there is any programme of new build in the UK.
"Openness and transparency must underpin everything that is done in this area."
Nirex spokesman David Wild said it would have broken the law to release the list during the election.
"Our legal advice was very clear. We had to try our best not to damage the future process."
But Rob Edwards, a journalist for the New Scientist and Sunday Herald, said: "It's just a sign of the inherent characteristic secrecy of the whole nuclear operation in the past.
"Nirex wanted to keep it out of the general election but they have now agreed and government ministers have agreed."
He said it was likely that the same sites would feature in any future discussions.
"If you are on the old list, you stand a very good chance of being on any new list."
Friends of the Earth's Chief Executive, Duncan McLaren, said: "The government needs to learn that the best way to begin dealing with the UK's nuclear waste legacy starts with halting the production of any more waste."