Staff at the White Bear pub, in Kingsley Road, were closing up for the night on Sunday July 31, at 2.11am, when the man walked off with the RNLI box in the shape of a lifeboat.
Manager Stephanie Nicholina Lewis said the box was nearly full and probably contained around £90 in cash.
"It's so bad. I can't believe anyone would steal from a charity like this," she said.
The pub's owner Tarrin Constantine released the footage in a bid to catch the man, who Ms Lewis said was not known to staff.
The money would have helped fund the Royal National Lifeboat Institution's life-saving operations on Britain's coast and rivers.
A lifeboat crew recently helped rescue nine people trapped on a boat in Chiswick which had caught fire.
Chiswick RNLI also came to the aid of a drunken tennis fan last month who celebrated Andy Murray's Wimbledon title by stripping off and jumping in the Thames.
Anyone with information is asked to call police on the non-emergency number 101. To remain anonymous, call Crimestoppers on 0800 555111.