The BBC’s Newsnight program said the archival documents showed a deal was done to export 20 tonnes of heavy water to Israel.
At the time ministers in Harold Macmillan’s government were apparently unaware of the deal, which was also kept secret from the US, the BBC said.
No “peaceful use only” conditions were imposed on the use of the heavy water – used for the production of plutonium – at the top-secret Dimona nuclear reactor in Israel’s Negev desert.
Former Conservative defence and foreign office minister Lord Gilmour said the revelations were “quite extraordinary”.
He said: “Whether the civil servants who were involved knew what they were doing, or whether they didn’t, I don’t know.
“One must assume they must have known and what’s more they seemed to have no idea of the political, or indeed even the technical and foreign-policy implications, of what they were doing,” he told the BBC.
In one of the documents Foreign Office official Donald Cape said: “On the whole I would prefer not to mention this to the Americans”.
The US had apparently refused to supply heavy water to Israel without a guarantee it would only be used for peaceful means.
Robert McNamara, US President John F Kennedy’s defence secretary from 1961, told Newsnight he was “astonished” at the apparent cover-up.
“The fact that Israel was trying to develop a nuclear bomb should not have come as any surprise,” he said.
“But that Britain should have supplied it with heavy water was indeed a surprise to me.”
Documents apparently show the heavy water – surplus from a consignment bought from Norway – was shipped from British to Israel.
Teh BBC said officials seem to have presented it as a deal between Norway and Israel.
The existence of the reactor and a probable nuclear weapons program in Israel was later exposed by the Daily Express newspaper, causing the Foreign Office to block the sale, the papers show.