In addition to the portrait, a collection of handwritten letters by Gandhi to the family of Sarat Chandra Bose, a freedom fighter and the elder brother of Subhas Chandra Bose, fetched 37,500 pounds at a Sotheby's auction.
"Gandhi usually refused to sit for formal photographs, let alone a portraitist, making this an extremely rare portrayal of the political leader at work," the auction house said in a statement.
The sketch shows Gandhi writing with a look of intense concentration whilst seated on the floor, and is inscribed by him with the words "Truth is God/MK Gandhi/4.12.'31'."
Gandhi stayed at Kingsley Hall at the time, a community centre in London's East End, at the invitation of one of its founders Muriel Lester who had previously stayed in Gandhi's ashram (hermitage) in India.
The pencil portrait, which was inscribed by Gandhi the day before he left Kingsley Hall, was given to a local resident who was closely associated with the hall throughout her life and has remained in her family ever since.
The portrait was estimated to fetch between 8,000 and 12,000 pounds while the letters were valued between 23,000 and 33,000 pounds.
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