Officers are growing increasingly concerned for the welfare of 25-year-old Zoe Grigsby was last seen leaving West Middlesex Hospital on Twickenham Road, Isleworth at around 2.30pm on Thursday (April 7).
The young woman is described as white, 5ft 8ins tall with shoulder-length brown hair and wears glasses.
She was last seen wearing black clothing.
Officers believe she could be in the Aldershot area of Hampshire.
Hounslow police are also continuing to appeal for help to find missing 64-year-old man Joao Nobrega from Feltham who was last seen on Sunday (April 3) when he left his home at Stone Crescent for a regular walk.
The search also continues as Ealing police appeal for help to find missing teenage boy Warfa Olad from Oxford Road in Ealing who was last seen at his home address almost two weeks ago on March 26.Anyone who has seen Zoe is asked to contact officers in Hounslow via 101 or contact the charity Missing People on 116000.