British Prime Minister David Cameron has gone out not with a bang, nor a whimper, but a mystery tune.

He appeared to be humming a little tune to himself as he walked away from cameras after announcing he would hand over power to his successor Theresa May on Wednesday.

Cameron stepped away still wearing his lapel microphone and could be heard singing to himself as he reached the door of 10 Downing Street, his official residence, in video footage broadcast by ITV.

As the door opened, he could be heard saying "Right!" before it closed behind him and a scratching sound was audible, indicating the microphone was removed.

"Do doooooooo, do doooo," he sang to himself, according to the clip sent by BBC reporter Daniel Sandford.

Moments earlier the departing Conservative Party leader had announced: "We'll have a new prime minister in that building behind me by Wednesday evening".

It wasn't immediately clear what tune Cameron was singing, but the social media world poured forth with often-satirical suggestions. One writer opined that Cameron had just unwittingly revealed the secret "Open Sesame" musical code for the Downing Street door.

Another theorized that it was Cameron's personal "game over" videogame hook.

Some thought they detected a hint of "The West Wing" theme tune.Soon, hastily remastered clips of Cameron's doings accompanied to the beats of Dr. Dre were doing the social media rounds.

Bloomberg's Rob Hutton said it sounded like the beginning of the theme song for the hit US political drama series "West Wing", while ITV's Robert Peston said it was just a "Winnie-the-Pooh style hum".