The men, aged 39 and 55, were picked up by officers from Scotland Yard's counter terrorism command.
Both are being held under the Extradition Act after being arrested at a residential address in west London.
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Addressing an audience in America, the former PM said of Europe's single currency that it was not working "as intended".
The countries lawmakers voted to impeach President Park Geun-hye in the wake of mass protests against her.
The former presidential candidate, who has herself been the target of false news reports, said such stories had 'real-world consequences'.