Police have said that the passengers watching the assault did not intervene because they thought the pair were a couple.
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The train was travelling from London Bridge to Chislehurst between 12.53am and 1.15am on Friday, July 18.
The victim was followed onto the train by a man who sat next to her. He then assaulted her for around 20 minutes before leaving.
Police are looking for the man seen below as part of their investigation.
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Detective Constable Andy Parkinson, of the British Transport Police, said: "There were a few people on the train at the time who may have thought the pair were a couple and were reluctant to step in.
"This was not the case and I am urging these people to come forward as they may have information crucial to our investigation.
"The man’s behaviour was totally unacceptable and inappropriate and we are currently following several lines of enquiry.
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Anyone with information can contact British Transport Police on 0800 40 50 40, or text 61016, quoting reference B8/SSUB of 15/08/2014.