Using testimony of those involved and declassified documents obtained under the US Freedom of Information Act, it said that despite a desperate search of the crash site near a US military base at Thule, the weapon was never found.

Built in the early 1950s, Thule Air Base was of great strategic importance to the United States in its Cold War stand-off with the Soviet Union, allowing a radar to scan the skies for missiles coming over the North Pole.

But Washington feared the Russians might destroy it as a prelude to a nuclear strike against the United States.

As a result the US military deployed nuclear-armed B52 bombers to circle over the base from 1960, so they could head straight to Moscow if it was destroyed, the British broadcaster reported.

However, on January 21, 1968, one of these planes crashed into the ice a few miles from the base. The explosives surrounding the four nuclear weapons on board detonated but the active nuclear devices did not, the BBC said.

Investigators recovered thousands of pieces of debris from the site, including ice containing radioactive debris, but soon realised that only three of the weapons had been accounted for.

An underwater search was launched in April but they found nothing and eventually the investigators gave up.

William H Chambers, a former nuclear weapons designer at the Los Alamos nuclear laboratory that ran the team dealing with the Thule crash, told the BBC there was "disappointment" at the failure to find all the plane's parts.

But he explained: "It would be very difficult for anyone else to recover classified pieces if we couldn't find them."

Officials also believed the radioactive material would dissolve in such a large body of water and be made harmless, the BBC said.

It said the carrying of nuclear weapons over Greenland, a self-governing province of Denmark, was kept a secret, as was the nature of the search.

The US Department of Defense declined to comment on the BBC's investigation, referring back to previous official studies of the incident. It previously said all four weapons had been "destroyed".