Previous reports have suggested that they may already be in a safe house in a country belonging to the "Five Eyes" security alliance comprising Britain, the United States, Canada, Australia and New Zealand.
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• Poisoned ex-Russian spy Sergei Skripal and daughter may be in safe house, possibly in New Zealand
• Suspected Russian assassins in Sergei Skripal saga ridiculed after claiming to have been tourists
• Russian spy's daughter Yulia Skripal poisoned 'days after gaining access to secret bank account'
• Police 'identify' Russian Novichok attackers who poisoned former spy Sergei Skripal and his daughter in Salisbury
Sergei Skripal, now 68, is a former Russian military intelligence officer who acted as a double agent for Britain in the 1990s and early 2000s.
He was caught and jailed in Russia in 2004, but was freed in a spy swap in 2010 which allowed him to move to Britain.
Mail on Sunday defence editor Mark Nicol reported today that, after two years "effectively living under house arrest" in Britain, Sergei and his daughter Yulia are now "desperate to leave the UK for either Australia or New Zealand".
"The Mail on Sunday has also received unconfirmed reports that Mr Skripal, 68, and his daughter, 35, may have already travelled to Australia and New Zealand to scout possible locations," Nicol reported.
British chemical weapons expert Hamish de Bretton-Gordon was quoted as saying: "I'm sure Yulia especially will want to return to some sort of normality and a remote Commonwealth country may be an option.
"The Government continues to have a duty of care and the Russians seem unconcerned with any collateral damage they caused around this assassination attempt. So security arrangements would in all certainty continue."
In September 2018 British authorities named two Russian agents using the names Alexander Petrov and Ruslan Boshirov as suspected of the Skripals' poisoning and charges were laid against them in absentia.
Nicol reported that the British Defence Ministry led the clean-up of the Skripals' house after the Novichok attack because of security concerns over leaving the job to contractors, who might have passed sensitive information to Russia.
A Defence Ministry spokesman said: "Due to the nature of the substance, the military were best equipped to lead the clean-up."