The toddler - who answers to the name Jack - was left at West Hampstead police station, north London, on Saturday afternoon while the front desk was briefly unattended, said Scotland Yard.
A blonde-haired woman hurried out of the lobby after leaving the crying boy in a blue Cindico pushchair with a holdall containing nappies and the child's bottle.
He was taken by ambulance to the Royal Free Hospital nearby for a medical examination, where doctors said he was "safe and well". Jack was described as aged between 18 months and two years, white, 2ft 6in tall with strawberry blond hair "with a hint of ginger" and blue eyes. He was wearing a grey hooded Gap top, jeans, Winnie the Pooh socks and black boots.
The woman who left him was described as white, aged about 25, wearing a blue anorak. The officer heading the hunt for Jack's family or carers, Detective Inspector Trevor Barnes, urged anyone with any information about his identity to come forward.
He added that Jack appeared undisturbed by his ordeal. "He is very bright and bubbly and responding well to those around him," said Mr Barnes. "He is not fazed at all. He is very happy." Jack, who appeared well fed and cared for, had been placed temporarily with a foster family.Reuse content