Gangs of youths armed with knives, hockey sticks and other weapons fought running battles across Trafalgar Square in 90 minutes of mayhem on Thursday.
Eyewitnesses said young men clashed violently on the pedestrianised area around Nelson’s Column and on nearby roads.
Dozens of police raced to the square and arrested 19 people, the youngest of whom was 14.
The three injured teenagers – one 18-year-old and two aged 19 – were taken to hospital with non- life-threatening injuries.
The fighting is believed to have involved rival gangs of Albanian Kosovans from several parts of the capital.
The fighting took place on the third anniversary of Kosovo’s declaration of independence from Serbia.
A police spokesman said the fighting broke out at around 4pm and the stabbings took place over the next 90 minutes.
Investigators have seized footage from several closed circuit TV and traffic cameras that cover the area around the square.
Supt Simon Ovens said: “This appears to have been a spontaneous incident and our officers were on scene extremely quickly, resulting in 19 people currently being held in custody.
“However, it is going to take some time for us to speak to them all and establish a clear picture of exactly what happened.
“Trafalgar Square is an incredibly busy place and I would urge anyone who was in the vicinity yesterday evening and may have seen something to come forward and talk to us.
“Their information could be vitally important in helping us to piece this incident together.
“This sort of violence will not be tolerated in any part of central London and will always result in a robust police response.”
Anyone with information should contact police on 0300 123 1212 or anonymously via Crimestoppers on 0800 555111.