Other newspapers, including the Guardian and the Daily Telegraph also reported on the extradition moves.
United Kingdom intelligence chiefs have specifically blamed Russian Federation for the attack.
An investigation by hundreds of British police and intelligence officers have pieced together the movements of the two Russians, from their entry into Britain through to their departure, the Guardian reported.
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Britain blamed Russian Federation for the poisonings and identified the poison as Novichok, a deadly group of nerve agents developed by the Soviet military in the 1970s and 1980s.
The Times reports said that an extradition application would reignite a diplomatic row with the Russian government who have denied any state involvement in the novichok attack in Salisbury.
"This is Litvinenko all over again".
They were both found unconscious on a bench in a shopping centre after being exposed to novichok - they were initially thought to have been intoxicated.
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Russian Federation has previously rejected similar extradition requests.
In 2007, President Vladimir Putin rejected an extradition request for two Russians suspected of the assassination of the former FSB officer Alexander Litvinenko in London using radioactive polonium.
The request will inflame the current diplomatic row Russian Federation.
British police believe the Novichok nerve agent used on Yulia and her former double agent father in March was the same chemical used to kill 44-year-old Dawn Sturgess and her partner Charlie Rowley in late June, about eight miles away.
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Police have said they believe the two incidents are related, theorizing that perpetrators first smeared the Novichok on the door of Sergei Skripal's house and discarded the container, which Rowley later picked up and gave to Sturgess, who sprayed it on her wrists.