In a video released by the Sun on Sunday, the footage also apparently showed Rev Stennett Kirby talking about buying poppers from a shop in Soho.
Purchasing poppers – a liquid which induced a head-rush high – is not a crime.
Hazy footage apparently showed the 64-year-old sitting on his sofa, saying “I feel really good now” after reportedly taking cocaine.
It’s alleged the video also shows Rev Kirby, who has been a vicar of West Ham Parish Church since 2007, watching pornography with a friend.
The Church of England told the Sun on Sunday it was investigating the footage, while a spokeswoman told the newspaper: “We take this matter very seriously.”
Rev Kirby, who is unmarried, has reportedly been placed on sick leave.
A spokesman for the Church of England said: “We are taking this matter very seriously.
“Revd Stennett Kirby has withdrawn from all ministerial duties and a disciplinary investigation is already under way.”
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The Church of England is said to be investigating after a newspaper published a video appearing to show a vicar from East London taking cocaine and watching explicit videos.