Recently declassified papers reveal a deal was done to export 20 tons of heavy water, an ingredient vital for plutonium production at the top-secret Dimona nuclear reactor in Israel's Negev desert.
No "peaceful use only" condition was placed on its use. Officials said imposing one would be "over zealous."
The deal was kept secret from the United States, which had refused to supply heavy water to Israel without a guarantee it would be used only for peaceful means.
Robert McNamara, U.S. Defense secretary in the 1960s, told BBC News he was "astonished" by the coverup.
"It is very surprising to me we were not told because we shared information about the nuclear bomb very closely with the British."
By the time Israel asked for more heavy water in 1961, the existence of the Dimona reactor and its probable weapons program had been exposed in the media, leading the Foreign Office to block the sale.
Israel has never admitted or denied having a weapons program, but refuses to sign the Nuclear Non-Proliferation Treaty.