Winston Churchill complained he had been "sold a pup" when he discovered his underground wartime headquarters in Whitehall were not bomb-proof.
A letter showing Churchill's annoyance when he discovered this security flaw is on display at the Cabinet War Rooms.
Despite his protests, the prime minister continued to work from this bunker during the Blitz.
The letter, written in September 1940, says the war rooms "cannot be made bomb-proof in any sense".
The Cabinet War Rooms, now open to the public, were used as an underground command centre throughout World War II.
Built close to Downing Street and the nerve centres of government departments, it allowed the prime minister to stay in central London during air-raids.
But an exhibition opening next month in the former headquarters, will show how vulnerable this building was to attack - and how fortunate it was never to have received a direct hit.
The letter, written by senior civil servant Patrick Duff to Cabinet Secretary Sir Edward Bridges, describes Churchill's shock at finding the weakness of the rooms used by the war cabinet and military leaders.
"The PM said I had 'sold him a pup' in letting him think that this place is a real bomb-proof shelter, whereas it is nothing of the kind," wrote Mr Duff.
The letter goes on to say that it is "totally impracticable to make anything of the nature of a bomb-proof dug-out within this building".
It meant that while Nazi leader Adolf Hitler operated from headquarters encased in layers of concrete, Churchill and his staff were sleeping in rooms only 10 feet below ground.
Exhibition curator Cressida Finch says the war rooms were "in effect a basement rather than a bunker".
"This whole episode tells us a lot about Churchill's personal bravery. Although he was angry on learning that the war rooms were not completely safe, he was determined not to leave central London and be seen as abandoning Londoners," she says.
There were several near misses during air raids. But, despite efforts to strengthen the building, including the placing of a reinforced concrete slab, there were doubts whether it would have withstood a direct hit.
"This letter certainly makes clear Churchill's surprise and indignation at being handed a potentially vulnerable bunker," says Phil Reed, director of the Churchill Museum and Cabinet War Rooms.
The underground control centre from which Churchill directed the war effort and communicated with allies such as President Franklin Roosevelt, had originally been the storage rooms of the Office of Works.
With the threat of war approaching, the basement was sandbagged and hastily converted into what was expected to be a temporary command centre, completed and made operational one week before Hitler invaded Poland in 1939.
This network of tunnels and offices grew in size and significance, becoming a political and military headquarters and living space for hundreds of staff.
The long hours spent underground meant that staff were required to use sun lamps.
Shut down at the end of the war, the rooms were re-opened as a museum in the 1980s.
The exhibition, Undercover: Life in Churchill's Bunker, opens on 27 August to mark the 70th anniversary of when the war rooms entered service.