The teenager had "serious underlying health problems" and tests carried out after he died confirmed that he had the A(H1N1) virus, an official said.
"It's with sadness that we have to announce the death of a patient in London who has subsequently tested positive for H1N1 swine flu," said Simon Tanner, director of public health for London.
No other details were released.
The three others who died also had serious pre-existing health problems before contracting the virus, officials have said.
News of the death comes one day after the British government warned that the country could soon face more than 100 000 daily cases of swine flu if the current rate of infection is maintained.
Health officials also said they have stopped trying to contain the virus, given the high number of cases, and were switching to focusing on treating those infected.
Britain already has Europe's highest number of reported cases with nearly 7 500.
AFP
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