British Prime Minister David Cameron has all-but handed over the reins of power to Theresa May, but his announcement has been upstaged by a little tune he hummed to himself when walking away from the cameras.

Still wearing his lapel microphone, Mr Cameron could be heard humming an upbeat tune as he re-entered 10 Downing Street, in footage broadcast on ITV.

As he opened the door, Mr Cameron was heard to say "Right! Good", before closing it behind him and removing the microphone.

Just moments earlier, Mr Cameron announced Ms May's succession was imminent.

"We'll have a new prime minister in that building behind me by Wednesday evening."

Following a divisive Brexit campaign and referendum — which did not go the way Mr Cameron wanted — it seemed an understated and suitably British manner to bow out.

But views on Twitter among political journalists over which song Mr Cameron may have been humming have been divided, with some saying it sounded like West Wing's theme tune, and ITV's Robert Peston saying it was just a "Winnie-the-Pooh style hum".

Others on Twitter thought it may have been a rendition of The Muppets' Mahna Mahna — it would not be the first time that classic tune has been covered.

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