The admission is 60 years overdue, yet it may take even longer for our government to own up.
The essential facts have long been known.
A concise but full summary can be found in Dilip Hiro's book Iran Today and a vivid account of the British involvement is given by the outstanding journalist Robert Fisk in The Great War for Civilisation.
The CIA documents now released are said to show how the British government in the 1970s tried to block the release of information about its own complicity.
The Guardian reports that on Monday of this week the British Foreign Office "could neither confirm nor deny Britain's involvement in the coup."
Christopher "Monty" Woodhouse, Britain's "information officer" in Tehran, told Robert Fisk in 1997 that in preparation for the coup he flew a truckload of guns and a couple of million pounds into Iran for the pro-Shah elements.
Another part of the operation was to bring back the Shah, who had fled the country, and to assure him of British and US support.
Woodhouse's US counterpart, Kermit Roosevelt, headed the US - and decisive - end of the operation. The US government was concerned that Mossadeq would throw in his lot with the Soviet Union.
The returned Shah, with his barbaric Savak secret police and their torture chambers in close support, was absolute monarch of Iran for the next 26 years and a dear friend of Western governments - with oil nationalisation in effect reversed - before popular revolution deposed him in 1979.
What clandestine British government machinations are at this moment on foot in relation to Syria, Egypt and elsewhere in the Middle East?
Do we have to wait for more whistleblowers to tell us what our governments are doing?