Winston Churchill complained he had been "sold a pup" when he discovered his underground wartime headquarters in Whitehall were not bomb-proof, BBC reported.
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.