Scotland Yard released an image of Kinane Rose after a woman, in her 80s, was held against her will at her address in Norbury, Croydon, for two hours on Monday.
A man claiming to be a gas meter reader visited the woman at her home.
When she questioned him, he physically restrained her and bundled her to the floor, where she was kept for two hours, police said.
The man fell asleep and the victim was able to shout for help from the front door.
Her attacker fled.
The woman was left shaken but unhurt by the incident and nothing was stolen, detective confirmed.
Rose, 23, was last seen on Thursday on a route 133 bus from London Bridge heading towards Brixton. He is believed to have travelled to Croydon.
Members of the public are urged not to approach Rose, and should call 999 if they see him.
Anyone with any information on Rose's whereabouts is urged to call police on 101.
To give information anonymously Crimestoppers can be contacted on 0800 555 111 or by visiting crimestoppers-uk.org.
