Carol Ewemade left home at around 8.30am on Monday to visit a friend in Peckham but it has been established she never arrived at her destination.
The 84 year old called her daughter to say she was lost and had been advised to get the 345 bus towards Walworth Road.
But her daughter has been unable to reach her since the midday call, leaving her family extremely worried.
Detective Sergeant Ben Cowen, from the South East area’s missing person unit, said: “We are very concerned for Carol’s welfare. This is extremely out of character for Carol and understandably her family are really worried.
“We are calling on the public to help us find Carol. Were you the kind member of public who told her what bus to get on?
“Maybe you were on the 345 bus yesterday afternoon and saw Carol if she got on? Any information you have could be vital to helping us find Carol, so please get in touch.”
Enquiries suggest Ms Ewemade was in the Norbury area in the early hours of Tuesday.
Carol is being described as a black woman, about 5ft2ins of medium to large build.
Her hair is black and braided with white in-braids.
She was last seen wearing grey jogging bottoms, a dark green winter coat with no hood, a white head scarf covering hair.
At the time, she was carrying a black strapped purse bag.
Anyone with any information is asked to call police on 101 or Tweet @MetCC and quote 22MIS005334. To report information anonymously, contact the independent charity Crimestoppers on 0800 555 111 or visit crimestoppers-uk.org.