Police have confirmed that the child who died following a collision in Kendal was a 10-year-old girl.
And specialist officers are continuing to support her family, who are from the town, Cumbria Constabulary said.
Police said at this time, there was no indication to suggest that the incident was a deliberate act.
Police were contacted at around 5pm yesterday, March 5, after a report of a collision involving a black BMW i4 and two children on a sports pitch at Kendal Rugby Union Football Club, Shap Road.
The second child, an eight-year-old girl from Kendal, was taken to hospital for treatment. Her injuries are not life-threatening.
A 40-year-old man, from Lancaster, was arrested on suspicion of causing death by dangerous driving. He remains in police custody.
Police said enquiries were continuing to establish the full circumstances of this incident and to inform a future coronial process.
A multi-agency response will continue today to support people affected by this incident, they added.
Anyone who directly witnessed the collision is asked to contact police by reporting online at www.cumbria.police.uk/report-it, quoting incident number 195 of 5 March or call 101.
Last night, police said they were treating the collision as an isolated incident and there was no suggestion that it was terror-related.
Chairman of Kendal Rugby Club, Dr Stephen Green, released a statement on the club’s Facebook page.
He said: “We are deeply saddened to confirm that an incident occurred today at Kendal Rugby Club, resulting in a tragic loss of a child’s life.
“Our thoughts are with their family and friends and we kindly ask for privacy for all involved at this difficult time.
“We are co-operating fully with the authorities as they conduct their investigation – the club and all facilities are temporarily closed while this is carried out.”
Westmorland & Lonsdale MP Tim Farron said: “This is devastating, utterly heartbreaking news. I’m praying for the children and for their families and friends. Our community in Kendal is stunned and in mourning.”
Local Westmorland & Furness councillors, Jonathan Cornthwaite and Shirley Evans issued a joint statement.
They said: “We are devastated by this event and our hearts go out to all of those affected from the families involved to those who witnessed this horrific event.
“I know we speak on behalf of the community when we say how shocked and distressed everyone is by this tragic incident and our thoughts are with all those affected, especially the families, at this sad time.
“We also want to thank everyone who responded so quickly from the paramedics to the police.”
