The artwork, of David Cameron and Boris Johnson in tails and yellow waistcoats as members of the elitist Oxford University dining club, was originally commissioned to get around copyright laws.
Now Oxfordshire’s Mallams will offer it at its December 8 auction carrying an estimate of £5000-£7000.
Oxford artist Rona Marsden was commissioned to paint the picture by political journalist Michael Crick nearly a decade ago.
The first publication of The Bullingdon Club photo featuring Cameron and Johnson appeared in 2007 in The Mail on Sunday.
BBC Newsnight, and later other media outlets, were keen to show the image but Gilman & Soame, the Oxford portrait photographers who hold the copyright, said they would no longer give permission to reproduce it.
So Crick decided to have a painting of the photo created that could be used instead.
Marsden said: “I was approached by Michael Crick on February 28 to paint, in great haste, a likeness of the Bullingdon Club portrait - one that the BBC could use in place of the photograph. I happened to have a 3ft x 4ft canvas primed and ready to use in my studio in Oxford, so I began that night.”
The Oxford dining and drinking club has a reputation for boisterous bad behaviour and was seen as an embarrassment for Cameron. He told the BBC’s Andrew Marr: “We do things when we are young that we deeply regret.”
Marsden was paid a small fee for her services and was eventually allowed to keep the picture.
The BBC has used it periodically over the past decade as have newspapers such as The Times, The Independent and The Observer.
Twelve prints of the painting have also been made, but being offered for sale is the original oil painting.
Marsden created tea towels from the image to sell and will retain the right to reproduce the image after the painting is sold.