Sarah Everard 33, was last seen at a friend's house in Clapham on the evening of March 3, which she left at around 9pm.
She is thought to have left Leathwaite Road through a back gate and walked across Clapham Common and was expected to arrive home around 50 minutes later, but she has not been seen or heard from since.
It is unclear if she returned to her home address, Metropolitan Police said.
Ms Everard was last seen wearing a green rain jacket, navy blue trousers with a white diamond pattern, and turquoise and orange trainers. She is thought to have been wearing green earphones and a white beanie hat, Scotland Yard added.
North Yorkshire Police has also shared the appeal to help find Ms Everard, saying she has links to York.
In a statement her family, who are thought to have travelled from York to London to assist with the search, said: “With every day that goes by we are getting more worried about Sarah.
“She is always in regular contact with us and with her friends and it is totally out of character for her to disappear like this. We long to see her and want nothing more than for her to be found safe and well.
“We are so grateful to the police and all our friends for all they are doing.
“We are desperate for news and if anyone knows anything about what has happened to her, we would urge you to please come forward and speak to the police. No piece of information is too insignificant.”
Detective Chief Inspector Ian Kenward said: “Sarah’s disappearance is completely out of character and understandably her family and friends are incredibly worried.
“We are also growing increasingly concerned for her welfare and have officers working round the clock to try and find her.
“I would ask anybody who was in the Clapham Common area on Wednesday night to think about whether you saw Sarah or any suspicious activity around the time of her disappearance.”
People who may have footage or were in the following areas are being urged to check cameras: the A205 South Circular around Clapham Common, Cavendish Road, New Park Road, Brixton Hill and Brixton Water Lane.
Anyone with information should call 101 quoting CAD 3309/06MAR, or call the Missing People charity anonymously on 116 000.