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 artwork was destined for an American museum until Cambridge’s Fitzwilliam Museum raised more than £1m to buy it.
Police are investigating after the historic sword was taken from Canna House on the Isle of Canna, which has 18 residents.
Aidan McAnespie, 23, was shot by a soldier in Co Tyrone in 1988.