A mother, father and two children were playing in Bushy Park, Hampton, when the dog ran over without a lead.
Police arrived at 5.44pm on 4 April to find a mother and her nine-year-old daughter suffering from deep bite wounds, the Met said.
The dog had also bitten the girl’s 10-year-old brother on the arm.
The family were treated by the London Ambulance Service before being taken to hospital.
Three men had been seen in the vicinity just before the attack, a Met spokeswoman said.
The individual believed to be the dog’s owner is described by police as a light-skinned black male with a moustache and hair on his chin, wearing a yellow and black top and black trousers.
It is thought the trio ran off towards Vicarage Road and anyone who recognises them is urged to contact police.