A resident of Dolphin Square has contracted the disease, according to Public Health England which said it was working with the management company to inform residents.
Officials said the resident who contracted the disease was “responding well” to treatment.
The 10-storey block of flats in Pimlico has a colourful past and has been described as London’s most famous apartment block.
During World War Two, “blackshirt” leader Oswald Mosley was arrested in his Dolphin Square flat and driven to prison. MI5’s Maxwell Knight recruited Ian Fleming to the Secret Service from a flat a few doors down. Former residents also include Princess Anne, Harold Wilson and Christine Keeler.
Charles de Gaulle based his Free France government in the square during the war.
A resident aged in her 60s, who asked not to be named, told the Standard: “We were only told about it today. There is only one person affected in a flat.
“It is not a disease that is easily spread around apparently so I am not too concerned.
“It’s something where bacteria is always there but sometimes this sort of thing happens.”
A student, 27, who lives in one of flats, said: “I’m quite freaked out about it. I have never experienced anything this before. “I called the management after getting an email and they said it was fine all fine.
She added: “I hope it is not a major issue and it is just one case but let’s hope we all don’t catch it. “I’m going down to the shops now to get Evian water until I know it has been sorted out.
“I’m taking that individual approach to safeguard against anything. My sister is a doctor and that’s what she recommended.”
It is understood that traces of the bacteria may have been found in one shower within the apartment blocks and that the water system is being tested on a daily basis.
Public Health England issued a statement saying: “PHE has been notified of a case of legionnaires’ disease at a domestic residence in central London. The person is responding to treatment, and PHE is working closely with the local authority and management company to inform and advise residents.
“Legionnaires’ disease is an illness caught by breathing in droplets of water containing bacteria which cause infection. Symptoms include fever, a persistent cough, breathing difficulties and chest pain. In severe cases it can cause pneumonia.”
Dolphin Square Limited confirmed that a resident had “recently been diagnosed with a respiratory illness caused by legionella bacteria.”
In a statement it said : “We are in contact with the affected resident and are providing ongoing support. As a precaution we have informed all of our residents and reissued guidance on the prevention measures that should be taken.
“We work closely with Feedwater, a leading water treatment specialist who oversee the monitoring and testing regime of our domestic water system and we are currently taking further advice and direction from Public Health England and the Local Authority.
“The health and welfare of everyone at Dolphin Square is central to all we do, which is why we invest heavily in ensuring that the water supply is safe and secure. Water at the Square is treated in accordance with all applicable national regulations and guidelines.”
A spokesman said the restaurant at the square remained open.
Last year residents of Dolphin Square criticised plans for a £400 million makeover that includes new rooftop penthouses.
US property company Westbrook plans to increase the number of apartments from 1,250 to 1,395 and want to demolish and rebuild the northern block, Rodney House.
Earlier this year an inquest heard how a woman died after contracting Legionnaires’ disease after staying at a hotel.
Elaine Brown, 69, from Liverpool, died from a stroke shortly after a visit to the Feathers in Ludlow, Shropshire in July 2017.
The jury heard she contracted Legionella pneumonia which contributed to the stroke.