The driver of the Land Rover, a woman aged in her 40s, has been arrested on suspicion of causing death by dangerous driving.

She stopped at the scene.

The incident, which saw officers, firefighters and paramedics, including London’s Air Ambulance, respond at around 9.54am on Thursday, is not being treated as terror-related.

Detective Chief Superintendent Clair Kelland, local police commander for south west London, said: “This is tragic news and our thoughts are with the girl’s family and friends, and everyone affected today.

“We remain at the scene and are continuing our investigation into the full circumstances of the incident.”

Police have announced that there have been further injuries and officers await an update from the London Ambulance Service.

Stephen Hammond MP for Wimbledon: “It is tragic to hear the news that a young girl has died following this morning's incident at The Study School.

“My thoughts are with the girl's family and friends.”

Wimbledon MP Stephen Hammond told the the PA news agency that several of those hurt were “critically injured”.

Police extended a large cordon around the school and television pictures from overhead showed the car up against the wall of the building, while firefighters and paramedics stood near a gap in the fencing at the entrance to the site.

Officers moved dog walkers and passers-by away from the scene as an air ambulance remained on the edge of the Common while a number of ambulances parked nearby.

Wimbledon resident Julie Atwood told the PA news agency: “My daughter used to go to this school. It’s a girls’ school.

“Wimbledon is like a little village. For this to happen in Wimbledon is unheard of. It’s terrible.”

The school, which costs £5,565 per term, is for girls aged four to 11 and sits on Wimbledon Common, just a mile away from the All England Lawn Tennis and Croquet Club as it hosts the world-famous tennis tournament.

Mr Hammond said the Camp Road site of the school caters for younger children between the ages of four and eight.