Molly Davidson, 19, from Sutton-in Ashfield, Nottinghamshire, has a mental age of 13 and epilepsy.
She was last seen at Nottingham's Broadmarsh bus station on Monday.
Her father Anthony said friends told him she had been chatting to a young man online for several months.
Mr Davidson said it appeared the pair had met on Facebook, where the man had multiple accounts, all of which have now been deleted.
He said the family had not heard anything from Molly since Monday and her devices were all offline, but phone tracking technology had shown she was in the capital.
Recent phone records also showed Molly had been talking to someone in the Edmonton area, so Mr Davidson and her mother Julie have travelled to the borough to distribute leaflets.
They said if Molly is not found soon, other family members will join them to cover a wider area.
The teenager was wearing black jeans and a cream jumper when she vanished.
Mr Davidson said: "Whatever she thinks she's done, we just want her to know she's not in any trouble.
"We just want her back safe and sound."
The family of a woman with learning difficulties who has been missing for four days believe she went to London to see a stranger she had met online.