Leonard Dunstan was last seen at around 5.35pm when he walked out of the emergency department at Charing Cross Hospital in Fulham Palace Road.
Mr Dunstan is described as black, 5ft 10 ins, medium build, with short grey curly hair balding on top.
When he disappeared he was wearing a black and white checked shirt, black trousers and he walks with a silver stick.
He has been known to spend time in the Fulham and Ealing areas.
The Metropolitan Police said they are particularly concerned for his welfare as he suffers from dementia and a range of other medical issues.
They are also concerned as temperatures have plummeted again with west London seeing snow on Friday and Saturday (February 10 and 11).
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