The Metropolitan Police had said they pulled a woman from the water after MP Stephen Gilbert claimed he rescued her:
"At 1950 the marine policing unit responded to reports of a woman in the River Thames near Westminster Bridge. They recovered her from the water and took her to hospital. Next of kin have been informed," the force said in a statement.
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The letter calls for an end to harassment, abuse, and impunity in a world "ripe for change".
Police say that anyone who sees Whitehouse should not approach him, but instead call them on 999 and quote incident 23 of 18 February.