Officers received reports shortly before July 30, detailing that a woman had given birth the same day at around 8am in the Billet Road underpass.
A witness reported she had been alerted to sounds of distress and stayed to aid with the woman with the birth.
She remained with the woman until around 4pm, when the mother and her newborn were picked-up by two people in a blue transit van.
According to the Metropolitan Police, they believe the missing woman is rough sleeping.
She is described as white, in her mid-30s, with long blonde hair.
She was seen wearing a black dress and heavy jumper, and is believed to go by the name Anne Marie.
Officers are “extremely concerned” for the welfare of both the woman and her infant.
PC Dan Cooper said: “Our top priority is to establish that the woman and her baby are safe and well and have access to any medical treatment they may need. I would like to stress that the woman is not in any trouble, our only concern is the wellbeing of her and her newborn child.
“We are carrying out fast-paced enquiries, including trawling CCTV, speaking to people in the area and visiting nearby hospitals.
“I’d also like to appeal to anyone who was in the area at the time and may have seen or heard something to come forward. Were you walking or cycling through the underpass or at the nearby Kwik Fit garage? If so, please get in touch with us.
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“If the woman does not feel comfortable speaking to us, she can go directly to a medical centre or a charity.”
Anyone with information is asked to call the North East area’s Local Missing Hub on 07881 330 956 or 101 quoting CAD 5617/30JUL.
Alternatively, you can contact the independent charity Crimestoppers anonymously on 0800 555 111 or visit crimestoppers-uk.org.