Matthew Patchen was last seen leaving his home in Crowndale Road on Friday (November 24).
The 25-year-old, who has been diagnosed with depression, spoke to his family by telephone on the evening of his disappearance and “was in some distress”.
His family are extremely concerned for his wellbeing, a spokesman for Metropolitan Police said.
Matthew is described as a white man of medium build, around 5ft 10 tall.
It is not known what he was wearing at the time of his disappearance.
The west London resident has family in Yorkshire and possibly an associate in south London.
It is believed Matthew may have been seen in the Euston Road area.
Police are asking anyone with information to call 101, or Holborn Missing Persons Unit on 0208 7336543 or 07881 330963.
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